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by sankofar » Fri Dec 04, 2009 11:39 pm
The perimeter of a certain isoceles triangle is 16 + 16√2. What's the length of the hypotenuse of the triangle ?

a) 8
b) 16
c) 16√2
d) 8√2

I thought answer should be D since it's a 45-45-90 angle but GMAT prep answer choice was B.
Any help with explanation would be helpful
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by okigbo » Sat Dec 05, 2009 1:30 pm
You're right... 45/45/90 - x+x+x *sq.rt.2 = 16+16*sq.rt.2

2x+x*sq.rt.2 = 16+16*sq.rt.2

Factor

x*sq.rt.2(sq.rt.2+1)=16(sq.rt.2+1)

x*sq.rt.2=16
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by bento » Mon Dec 07, 2009 10:41 am
I believe the question does refer to a 45-45-90 angle triangle with sides (x) - (x) - (x * Root 2). If you take your answer of (8 * Root 2), that means the two equal sides are 8 and the hypotenuse is equal to (8 * Root 2). Adding the 3 sides of the perimeter gives you 16 + (8 * Root 2) which is not the perimeter that the question is asking for.

Since you are looking for two sides of the triangle to be equal, the two equal sides must add up to (16 * Root 2). Therefore each equal side is (8 * Root 2) and the hypotenuse is equal to 16. Using the pythag theorem (a^2 + b^2 = c^2) or c = Root [(a^2) + (b^2)] to check your answer, you get Root [(8 * Root 2)^2 + (8 * Root 2)^2] which is equal to Root (64*2 + 64*2) = Root (256) = 16.

I hope that's the correct approach.
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by biker317 » Tue Dec 08, 2009 1:36 am
what bento is saying is right..but when I tried to solve it algebraically i got

x+x+xroot2=16+16root2

as we know the sides are in the ratio of 1:1:root2

so i got x=8 BUT this doesnt add up to the perimeter, somethings wrong with my approach, dont know what it is :(
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by aspirant1 » Tue Dec 08, 2009 4:33 pm
I am wondering why the triangle should be 45:45:90, it can be any other angle too may be 70:70:40 any thoughts?
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by Gundy » Tue Dec 08, 2009 6:09 pm
This question can be solved with the rule which states: "The length of any side of a triangle is less than the sum of the lengths of the other two sides". The two options for an isoceles triangle that has perimeter 16+16root2 are 8:8:16root2 or 8root2:8root2:16. The latter is the combination that satisfies the rule stated above: 8+8<16root2 while 2(8root2)>16.

From what I have gathered, a good deal of questions are based on knowledge of rules like this rather than actually solving the algebra/geometry.
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