Is this answer explanation correct?












4












$begingroup$


I took an IQ test for fun recently, but I take issue with the answer to one of the questions. Here's the question:



enter image description here



My issue is that the explanation assumes angle DC is a right angle. Given that assumption, I can see the quadrilateral is indeed a rectangle and a right triangle and can follow their explanation. However, (from what I remember my high school geometry teacher telling me) even though an angle looks like a right angle, it shouldn't be assumed unless it is explicitly stated or you can prove it. To explain what I mean, if DC isn't a right angle and we exacerbated that difference, it would look like the following:



enter image description here



Thus, even being given A, B, C and D it seems like the area could not be calculated.



So my question is twofold:




  1. Is my criticism valid or am I just being too proud because I got a question wrong?

  2. Given my interpretation, DC is not a right angle, can this problem be solved?






geometry







share|cite|improve this question









New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
    $endgroup$
    – fleablood
    2 hours ago






  • 1




    $begingroup$
    Not that angle, the one below it.
    $endgroup$
    – Robert Israel
    2 hours ago






  • 1




    $begingroup$
    Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
    $endgroup$
    – fleablood
    2 hours ago












  • $begingroup$
    " even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
    $endgroup$
    – fleablood
    2 hours ago
















4












$begingroup$


I took an IQ test for fun recently, but I take issue with the answer to one of the questions. Here's the question:



enter image description here



My issue is that the explanation assumes angle DC is a right angle. Given that assumption, I can see the quadrilateral is indeed a rectangle and a right triangle and can follow their explanation. However, (from what I remember my high school geometry teacher telling me) even though an angle looks like a right angle, it shouldn't be assumed unless it is explicitly stated or you can prove it. To explain what I mean, if DC isn't a right angle and we exacerbated that difference, it would look like the following:



enter image description here



Thus, even being given A, B, C and D it seems like the area could not be calculated.



So my question is twofold:




  1. Is my criticism valid or am I just being too proud because I got a question wrong?

  2. Given my interpretation, DC is not a right angle, can this problem be solved?






geometry







share|cite|improve this question









New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
    $endgroup$
    – fleablood
    2 hours ago






  • 1




    $begingroup$
    Not that angle, the one below it.
    $endgroup$
    – Robert Israel
    2 hours ago






  • 1




    $begingroup$
    Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
    $endgroup$
    – fleablood
    2 hours ago












  • $begingroup$
    " even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
    $endgroup$
    – fleablood
    2 hours ago














4












4








4





$begingroup$


I took an IQ test for fun recently, but I take issue with the answer to one of the questions. Here's the question:



enter image description here



My issue is that the explanation assumes angle DC is a right angle. Given that assumption, I can see the quadrilateral is indeed a rectangle and a right triangle and can follow their explanation. However, (from what I remember my high school geometry teacher telling me) even though an angle looks like a right angle, it shouldn't be assumed unless it is explicitly stated or you can prove it. To explain what I mean, if DC isn't a right angle and we exacerbated that difference, it would look like the following:



enter image description here



Thus, even being given A, B, C and D it seems like the area could not be calculated.



So my question is twofold:




  1. Is my criticism valid or am I just being too proud because I got a question wrong?

  2. Given my interpretation, DC is not a right angle, can this problem be solved?






geometry







share|cite|improve this question









New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I took an IQ test for fun recently, but I take issue with the answer to one of the questions. Here's the question:



enter image description here



My issue is that the explanation assumes angle DC is a right angle. Given that assumption, I can see the quadrilateral is indeed a rectangle and a right triangle and can follow their explanation. However, (from what I remember my high school geometry teacher telling me) even though an angle looks like a right angle, it shouldn't be assumed unless it is explicitly stated or you can prove it. To explain what I mean, if DC isn't a right angle and we exacerbated that difference, it would look like the following:



enter image description here



Thus, even being given A, B, C and D it seems like the area could not be calculated.



So my question is twofold:




  1. Is my criticism valid or am I just being too proud because I got a question wrong?

  2. Given my interpretation, DC is not a right angle, can this problem be solved?






geometry




geometry






share|cite|improve this question









New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 2 hours ago









Blue

49.3k870157




49.3k870157






New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









Jack O.Jack O.

21




21




New contributor




Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Jack O. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • $begingroup$
    You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
    $endgroup$
    – fleablood
    2 hours ago






  • 1




    $begingroup$
    Not that angle, the one below it.
    $endgroup$
    – Robert Israel
    2 hours ago






  • 1




    $begingroup$
    Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
    $endgroup$
    – fleablood
    2 hours ago












  • $begingroup$
    " even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
    $endgroup$
    – fleablood
    2 hours ago


















  • $begingroup$
    You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
    $endgroup$
    – fleablood
    2 hours ago






  • 1




    $begingroup$
    Not that angle, the one below it.
    $endgroup$
    – Robert Israel
    2 hours ago






  • 1




    $begingroup$
    Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
    $endgroup$
    – fleablood
    2 hours ago












  • $begingroup$
    " even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
    $endgroup$
    – fleablood
    2 hours ago
















$begingroup$
You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
$endgroup$
– fleablood
2 hours ago




$begingroup$
You know it is a right angle because it has a large "90" on it. Now we can argue they never said why it has a "90" on it and as I am a nitpick I would agree with you... but... I think you and I would lose in any court.
$endgroup$
– fleablood
2 hours ago




1




1




$begingroup$
Not that angle, the one below it.
$endgroup$
– Robert Israel
2 hours ago




$begingroup$
Not that angle, the one below it.
$endgroup$
– Robert Israel
2 hours ago




1




1




$begingroup$
Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
$endgroup$
– fleablood
2 hours ago






$begingroup$
Oh. Just reread. The question is utter bullshit and completely wrong and the person who wrote the answer is a complete idiot. You are correct.
$endgroup$
– fleablood
2 hours ago














$begingroup$
" even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
$endgroup$
– fleablood
2 hours ago




$begingroup$
" even though an angle looks like an angle, it shouldn't be assumed" but it doesn't even look like a right angle.
$endgroup$
– fleablood
2 hours ago










3 Answers
3






active

oldest

votes


















4












$begingroup$

You are right. The provided explanation is nonsensical. $DC$ cannot be assumed to be a right angle.



However, if you don't make that assumption, and take $BC$ as the only given right angle, the correct answer is "All four sides must be known."



The quadrilateral can be decomposed into two non-overlapping triangles. The first is a right angled triangle formed by sides $B$, $C$ and a hypotenuse, and its area is easy to determine. You can use Pythagoras' Theorem to find the hypotenuse of that right triangle formed by sides $B$ and $C$. That hypotenuse, together with sides $A$ and $D$ forms the other triangle. Its area can be computed using Heron's formula. Just sum the areas.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Perfect, thank you!
    $endgroup$
    – Jack O.
    2 hours ago










  • $begingroup$
    You're welcome.
    $endgroup$
    – Deepak
    2 hours ago



















2












$begingroup$

You are right: there is absolutely no indication that angle $DC$ is a right angle. If they wanted you to assume it was a right angle, they should have indicated that with another $90$. It really doesn't even look like a right angle (somebody had the bright idea of trying to render the picture in perspective, but we don't even know where the horizon is supposed to be).






share|cite|improve this answer









$endgroup$













  • $begingroup$
    That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
    $endgroup$
    – Jack O.
    2 hours ago










  • $begingroup$
    @JackO. See my answer. The correct answer would be "All sides must be known".
    $endgroup$
    – Deepak
    2 hours ago










  • $begingroup$
    If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
    $endgroup$
    – fleablood
    2 hours ago



















0












$begingroup$

You are correct that the given solution is wrong. Worse still, even if you know that the angles between BC and CD are both right-angles, the purported answer is still wrong! This is because if you're given the lengths of A,B,C, it still does not uniquely determine D because we are not told that the angle between AB is less than $90°$.






share|cite|improve this answer









$endgroup$














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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    4












    $begingroup$

    You are right. The provided explanation is nonsensical. $DC$ cannot be assumed to be a right angle.



    However, if you don't make that assumption, and take $BC$ as the only given right angle, the correct answer is "All four sides must be known."



    The quadrilateral can be decomposed into two non-overlapping triangles. The first is a right angled triangle formed by sides $B$, $C$ and a hypotenuse, and its area is easy to determine. You can use Pythagoras' Theorem to find the hypotenuse of that right triangle formed by sides $B$ and $C$. That hypotenuse, together with sides $A$ and $D$ forms the other triangle. Its area can be computed using Heron's formula. Just sum the areas.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Perfect, thank you!
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      You're welcome.
      $endgroup$
      – Deepak
      2 hours ago
















    4












    $begingroup$

    You are right. The provided explanation is nonsensical. $DC$ cannot be assumed to be a right angle.



    However, if you don't make that assumption, and take $BC$ as the only given right angle, the correct answer is "All four sides must be known."



    The quadrilateral can be decomposed into two non-overlapping triangles. The first is a right angled triangle formed by sides $B$, $C$ and a hypotenuse, and its area is easy to determine. You can use Pythagoras' Theorem to find the hypotenuse of that right triangle formed by sides $B$ and $C$. That hypotenuse, together with sides $A$ and $D$ forms the other triangle. Its area can be computed using Heron's formula. Just sum the areas.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Perfect, thank you!
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      You're welcome.
      $endgroup$
      – Deepak
      2 hours ago














    4












    4








    4





    $begingroup$

    You are right. The provided explanation is nonsensical. $DC$ cannot be assumed to be a right angle.



    However, if you don't make that assumption, and take $BC$ as the only given right angle, the correct answer is "All four sides must be known."



    The quadrilateral can be decomposed into two non-overlapping triangles. The first is a right angled triangle formed by sides $B$, $C$ and a hypotenuse, and its area is easy to determine. You can use Pythagoras' Theorem to find the hypotenuse of that right triangle formed by sides $B$ and $C$. That hypotenuse, together with sides $A$ and $D$ forms the other triangle. Its area can be computed using Heron's formula. Just sum the areas.






    share|cite|improve this answer









    $endgroup$



    You are right. The provided explanation is nonsensical. $DC$ cannot be assumed to be a right angle.



    However, if you don't make that assumption, and take $BC$ as the only given right angle, the correct answer is "All four sides must be known."



    The quadrilateral can be decomposed into two non-overlapping triangles. The first is a right angled triangle formed by sides $B$, $C$ and a hypotenuse, and its area is easy to determine. You can use Pythagoras' Theorem to find the hypotenuse of that right triangle formed by sides $B$ and $C$. That hypotenuse, together with sides $A$ and $D$ forms the other triangle. Its area can be computed using Heron's formula. Just sum the areas.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 hours ago









    DeepakDeepak

    17.7k11539




    17.7k11539












    • $begingroup$
      Perfect, thank you!
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      You're welcome.
      $endgroup$
      – Deepak
      2 hours ago


















    • $begingroup$
      Perfect, thank you!
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      You're welcome.
      $endgroup$
      – Deepak
      2 hours ago
















    $begingroup$
    Perfect, thank you!
    $endgroup$
    – Jack O.
    2 hours ago




    $begingroup$
    Perfect, thank you!
    $endgroup$
    – Jack O.
    2 hours ago












    $begingroup$
    You're welcome.
    $endgroup$
    – Deepak
    2 hours ago




    $begingroup$
    You're welcome.
    $endgroup$
    – Deepak
    2 hours ago











    2












    $begingroup$

    You are right: there is absolutely no indication that angle $DC$ is a right angle. If they wanted you to assume it was a right angle, they should have indicated that with another $90$. It really doesn't even look like a right angle (somebody had the bright idea of trying to render the picture in perspective, but we don't even know where the horizon is supposed to be).






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      @JackO. See my answer. The correct answer would be "All sides must be known".
      $endgroup$
      – Deepak
      2 hours ago










    • $begingroup$
      If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
      $endgroup$
      – fleablood
      2 hours ago
















    2












    $begingroup$

    You are right: there is absolutely no indication that angle $DC$ is a right angle. If they wanted you to assume it was a right angle, they should have indicated that with another $90$. It really doesn't even look like a right angle (somebody had the bright idea of trying to render the picture in perspective, but we don't even know where the horizon is supposed to be).






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      @JackO. See my answer. The correct answer would be "All sides must be known".
      $endgroup$
      – Deepak
      2 hours ago










    • $begingroup$
      If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
      $endgroup$
      – fleablood
      2 hours ago














    2












    2








    2





    $begingroup$

    You are right: there is absolutely no indication that angle $DC$ is a right angle. If they wanted you to assume it was a right angle, they should have indicated that with another $90$. It really doesn't even look like a right angle (somebody had the bright idea of trying to render the picture in perspective, but we don't even know where the horizon is supposed to be).






    share|cite|improve this answer









    $endgroup$



    You are right: there is absolutely no indication that angle $DC$ is a right angle. If they wanted you to assume it was a right angle, they should have indicated that with another $90$. It really doesn't even look like a right angle (somebody had the bright idea of trying to render the picture in perspective, but we don't even know where the horizon is supposed to be).







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 hours ago









    Robert IsraelRobert Israel

    330k23219473




    330k23219473












    • $begingroup$
      That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      @JackO. See my answer. The correct answer would be "All sides must be known".
      $endgroup$
      – Deepak
      2 hours ago










    • $begingroup$
      If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
      $endgroup$
      – fleablood
      2 hours ago


















    • $begingroup$
      That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
      $endgroup$
      – Jack O.
      2 hours ago










    • $begingroup$
      @JackO. See my answer. The correct answer would be "All sides must be known".
      $endgroup$
      – Deepak
      2 hours ago










    • $begingroup$
      If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
      $endgroup$
      – fleablood
      2 hours ago
















    $begingroup$
    That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
    $endgroup$
    – Jack O.
    2 hours ago




    $begingroup$
    That's what I thought. It should explicitly state if any angles are right. However my second question remains, given DC is ambiguous, is this question solvable? I don't think there would be enough information to solve in this case.
    $endgroup$
    – Jack O.
    2 hours ago












    $begingroup$
    @JackO. See my answer. The correct answer would be "All sides must be known".
    $endgroup$
    – Deepak
    2 hours ago




    $begingroup$
    @JackO. See my answer. The correct answer would be "All sides must be known".
    $endgroup$
    – Deepak
    2 hours ago












    $begingroup$
    If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
    $endgroup$
    – fleablood
    2 hours ago




    $begingroup$
    If we know all four lengths and assume no angle is more than 180, then I think there is only one quadrilateral so the area will be unique. I think. But you need all four. If you only three the fourth can be many lengths if the third one "swings".
    $endgroup$
    – fleablood
    2 hours ago











    0












    $begingroup$

    You are correct that the given solution is wrong. Worse still, even if you know that the angles between BC and CD are both right-angles, the purported answer is still wrong! This is because if you're given the lengths of A,B,C, it still does not uniquely determine D because we are not told that the angle between AB is less than $90°$.






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      You are correct that the given solution is wrong. Worse still, even if you know that the angles between BC and CD are both right-angles, the purported answer is still wrong! This is because if you're given the lengths of A,B,C, it still does not uniquely determine D because we are not told that the angle between AB is less than $90°$.






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        You are correct that the given solution is wrong. Worse still, even if you know that the angles between BC and CD are both right-angles, the purported answer is still wrong! This is because if you're given the lengths of A,B,C, it still does not uniquely determine D because we are not told that the angle between AB is less than $90°$.






        share|cite|improve this answer









        $endgroup$



        You are correct that the given solution is wrong. Worse still, even if you know that the angles between BC and CD are both right-angles, the purported answer is still wrong! This is because if you're given the lengths of A,B,C, it still does not uniquely determine D because we are not told that the angle between AB is less than $90°$.







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        answered 1 hour ago









        user21820user21820

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