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# Hypotenuse

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Joined: 01 May 2008
Posts: 114
Location: São Paulo
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Kudos [?]: 5 [0], given: 0

Hypotenuse [#permalink]  04 May 2008, 15:42
Can anyone help me with this question?

Tks
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Joined: 20 Feb 2008
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Schools: Kellogg Class of 2011
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Re: Hypotenuse [#permalink]  04 May 2008, 16:39
For starters you know two sides are equal since a right isoceles triangle has two equal sides. The perimeter formula for a triangle is A + B + C = P or for this problem: 16 + 16√2 = P Also, you know the sides are in the ratio 1:1:√2. So there are two possible answers:

1. The two short sides of the triangle add up to 16. Thus the hypotenuse is 16√2. We can check by using the pythagorean theorem.

8^2 + 8^2 = (16√2)^2

64 + 64 = (256 * 2), obviously this does not add up

2. The second option is that 16 is the hypotenuse and (16√2) is the length of each short side. Therefore each side would be 8√2.

(8√2)^2 + (8√2)^2 = 16^2

128 + 128 = 256, which is the correct answer.

Therefore the correct answer is B, 16.
Re: Hypotenuse   [#permalink] 04 May 2008, 16:39
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