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# Two Triangles Leaning Against Same Wall - question

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Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 00:10
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Please see attached picture of the problem.

When two triangles lean against the same wall, why are their hypotenuse the same?
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Re: Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 03:59
capstone207 wrote:
Please see attached picture of the problem.

When two triangles lean against the same wall, why are their hypotenuse the same?

why are you asking that the hypotenuse are the same? I think, the answer could be (C). You need the 2 statements!

Cheers!
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Re: Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 04:06
(D) Either will work.

You know that the board is the same size. If you have LN then you know that the sides are 1:1:root2. If you have the other one, you know that the triangle is 1:2:root3. Once you get the first hypotenuse, you should be able to get the second triangles sides. Then just compare the heights of the triangles.
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Re: Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 04:49
According to the question, line segment JK and LM represent two positions of the same board leaning against the side KN of a wall. So the hypotenuse of both the triangles is same.
Using 30:60:90 degree triangle and 45:45:90 degree triangle theorems, we can find out the answers using each statement alone.

Please let me know if you want me to explain further.
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Re: Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 05:52
1
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hgp2k wrote:
According to the question, line segment JK and LM represent two positions of the same board leaning against the side KN of a wall. So the hypotenuse of both the triangles is same.
Using 30:60:90 degree triangle and 45:45:90 degree triangle theorems, we can find out the answers using each statement alone.

Please let me know if you want me to explain further.

Yes, I see! Thanks!
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Re: Two Triangles Leaning Against Same Wall - question [#permalink]

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23 Sep 2009, 08:33
1
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hgp2k wrote:
According to the question, line segment JK and LM represent two positions of the same board leaning against the side KN of a wall. So the hypotenuse of both the triangles is same.
Using 30:60:90 degree triangle and 45:45:90 degree triangle theorems, we can find out the answers using each statement alone.

Please let me know if you want me to explain further.

Thanks hgp2k and aj1545 !! I missed the "same board", read it too quickly.
I was starting to think I had missed a geometry law lecture back in high school.
Re: Two Triangles Leaning Against Same Wall - question   [#permalink] 23 Sep 2009, 08:33
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