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GMATPrep exam question

by kiwitaker » Tue Aug 09, 2011 11:44 pm
Perimeter of a Right Isoceles triangle is 16+16root2.. what is the length of the hypotenuse?

A - 8
B - 16
C - 4root2
D - 8root2
E - 16root2

My answer was 8root2.. I thought that since ratio of the sides in an isoceles right triagle is 1:1:root2, i figured that "16" must correspond to the sum of the 2 equal sides.. with that assumption ended up with "D" as my selection..

The correct answer according to GMAT is B. Could someone please help explain the answer to me? I really dont know how that works.
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by Frankenstein » Tue Aug 09, 2011 11:51 pm
Hi,
If your hypotenuse is 8root2, sum of sides will be 8+8+8root2 = 16+8root2, not 16+16root2
If the 3 sides are a,a,aroot2, sum of sides = a+a+aroot2 = a(2+root2)=aroot2(root2+1) = hypotenuse(1+root2)
Here, hypotenuse(1+root2) = (16+16root2) = 16(1+root2)
So, hypotenuse = 16.
Cheers!

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by kiwitaker » Wed Aug 10, 2011 12:23 am
Aha! thanks for the quick reply Frankenstein! Much appreciated :-)
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by GMATGuruNY » Wed Aug 10, 2011 2:10 am
kiwitaker wrote:Perimeter of a Right Isoceles triangle is 16+16root2.. what is the length of the hypotenuse?

A - 8
B - 16
C - 4root2
D - 8root2
E - 16root2

My answer was 8root2.. I thought that since ratio of the sides in an isoceles right triagle is 1:1:root2, i figured that "16" must correspond to the sum of the 2 equal sides.. with that assumption ended up with "D" as my selection..

The correct answer according to GMAT is B. Could someone please help explain the answer to me? I really dont know how that works.
I posted a solution here:

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