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# The perimeter of a certain

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Manager
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The perimeter of a certain [#permalink]

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17 Dec 2008, 17:03
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The perimeter of a certain isosceles right triangle is $$16 + 16\sqrt{2}$$. What is the length of the hypotenuse of the triangle?

(A) $$8$$
(B) $$16$$
(C) $$4\sqrt{2}$$
(D) $$8\sqrt{2}$$
(E) $$16\sqrt{2}$$

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17 Dec 2008, 17:20
B = 16

Right angled Isoc, triangle sides are in the ratio x:x: sqrt(2)x

So, x+x+sqrt(2)x = 16 + 16*sqrt(2)

x = (16+16*sqrt(2))/ (2+sqrt(2))

We need to find out sqrt(2)*x and when you solve the above equation, it comes out as 16

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17 Dec 2008, 17:39
smarinov wrote:
Attachment:
Q1.JPG

$$2x+sqrt(2)x = 16+16 *sqrt(2)$$

$$sqrt(2)*x(1+sqrt(2)) = 16(1+*sqrt(2))$$

$$sqrt(2)*x=16$$
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Re: Perimeter   [#permalink] 17 Dec 2008, 17:39
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