hemant_rajput wrote:The perimeter of a certain isosceles right triangle is 32 + 32√2. What is the length of the hypotenuse of the triangle?
(A)16
(B)32
(C)8 root(3)
(D)8 root(2)
(E)16 root(2)
The sides of an isosceles right triangle are proportioned: s : s : s√2.
So if s=side and h=hypotenuse, then h = s√2 and s = h/√2.
We can plug in the answers, which represent the hypotenuse.
The correct answer is unlikely to be C, since √3 is not a value typically attributed to an isosceles right triangle.
Answer choice D: h = 8√2
s = (8√2)/√2 = 8.
p = 8 + 8 + 8√2 = 16 + 8√2.
Eliminate D. The perimeter needs to be quite a bit larger.
Answer choice B: h = 32
s = 32/√2 = (32*√2)/(√2*√2) = (32√2)/2 = 16√2.
p = 16√2 + 16√2 + 32 = 32 + 32√2. Success!
The correct answer is
B.
Last edited by
GMATGuruNY on Thu Jul 18, 2013 2:13 am, edited 1 time in total.
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