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# GEOMETRY QUESTION

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GEOMETRY QUESTION [#permalink]  14 Oct 2008, 09:37
Hello,

What is the value of the hypotenuse of an isosceles triangle with a perimeter equal to 16 + 16√2?

a. 8
b. 16
c. 8√2
d. 16√2
e. 32

Please help. I know it's pretty simple but I can't seem to wrap my head around it. Also, the GMAT practice test from GMAC says it's 16 but 8√2 is the only answer that makes sense to me.

Nevertheless, please teach me how to solve for this.

Thanks,

Elizabeth
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Intern
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Re: GEOMETRY QUESTION [#permalink]  14 Oct 2008, 10:11
2
KUDOS

Do you remember following rule?

isoscelss triangle rule

= 1:1: √2

= x : x : x √2

= x√2 : x√2 : 2x

then perimeter (P)

= x√2 + x√2 + 2x

= 2x√2 + 2x

Now, apply 16√2 + 16 = 2x√2 + 2x, and solve for x, which would be 8

Now you have all sides of triagles: = 8√2 : 8√2 : 16

In an isosceles right triangle, hypontenuse is the longest of sides
(or in x√2 : x√2 : 2x, whatever is equivalent to 2x), which is 16

hypotenuse is 16

(To double check)
if x = 8,

= x√2 + x√2 + 2x

= 8√2 + 8√2 + 16

= 16√2 + 16

Give me Kudos, Kudos, Kudos!!
Director
Joined: 23 May 2008
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Re: GEOMETRY QUESTION [#permalink]  14 Oct 2008, 10:20
since the question says hypotenuse, must mean that it is a right isoceles there for perimeter is x + x + xsqrt2

so 2x + xsqrt2 = 16 + 16sqrt2

x(2 + sqrt2) = 16 + 16sqrt2

x= 16 + 16sqrt2/2 + sqrt2

x=16(1+sqrt2)/2(1+sqrt2/2)

x=8(1+sqrt2)/1+sqrt2/2

x=8(1+sqrt2)*2/1+sqrt2

x=16
Manager
Joined: 15 Apr 2008
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Re: GEOMETRY QUESTION [#permalink]  14 Oct 2008, 10:51
Poots wrote:
Hello,

What is the value of the hypotenuse of an isosceles triangle with a perimeter equal to 16 + 16√2?

a. 8
b. 16
c. 8√2
d. 16√2
e. 32

Please help. I know it's pretty simple but I can't seem to wrap my head around it. Also, the GMAT practice test from GMAC says it's 16 but 8√2 is the only answer that makes sense to me.

Nevertheless, please teach me how to solve for this.

Thanks,

Elizabeth

this is a right isosceles triangle. so 2 sides have to be equal. if you take 8 underoot 2 as the equal side then you get 16 as the hypotenuse, but if you take 8 as one of the equal sides then you get 8 underoot 2 as the hypotenuse and perimeter as 16 + 8underoot 2.
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Re: GEOMETRY QUESTION [#permalink]  14 Oct 2008, 14:31
bigtreezl, thanks for the explanation. It makes perfect sense!
Intern
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Re: GEOMETRY QUESTION [#permalink]  14 Oct 2008, 14:32
and thanks to all others who posted a response.
Re: GEOMETRY QUESTION   [#permalink] 14 Oct 2008, 14:32
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