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Geo - Rt triangle

Expert replies
by hemant_rajput » Thu Jul 04, 2013 9:58 am
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)
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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Source: — Problem Solving |

by Brent@GMATPrepNow » Thu Jul 04, 2013 10:16 am
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)
EDIT: I deleted my post. I had assumed that the question was identical to this popular question:
https://www.beatthegmat.com/relation-bet ... tml#700804

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Nov 06, 2013 6:54 am, edited 1 time in total.
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by Brent@GMATPrepNow » Thu Jul 04, 2013 10:34 am
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)
EDIT: I deleted my post. I had assumed that the question was identical to this popular question:
https://www.beatthegmat.com/relation-bet ... tml#700804

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Nov 06, 2013 6:55 am, edited 1 time in total.
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by GMATGuruNY » Thu Jul 04, 2013 10:37 am
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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by kuzzden » Wed Jul 10, 2013 12:31 am
Hi, maybe simple algebraic method will also help:

Since the triangle is isosceles, its P = 2x + y
since it is right y*y = 2x*x, since all values are positive
x= y / sqr(2) = y*sqr(2)/2

Finally, after substitution we get P = y + y* sqr(2) = 32 + 32*sqr(2)
So, y = 32
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by macattack » Thu Jul 18, 2013 1:22 am
Hi experts,
you gave two dissimilar answers!!!! I think Mitch got it right!
Cheers
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