I think the image is a bit too small... Let me write the question down...

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)

The question tells you that it is an isoceles right triangle. In an isoceles triangle, 2 sides are equal. Thus, we can deduce that this is a 45-45-90 triangle.

Labeling the triangle, one side is x, the other side is also x, the hypotenuse is x(square root)2. Based on properties of 45-45-90 triangles.

THe question tells you that the perimeter is equal to 16+16(square root)2. Set that equal to how you labeled the figure. So x+x+x(square root)2 = 16+16(square root)2.

From here you can see that the value is 16.

Thanks for your reply...

I did the same approach when doing this problem, x + x + x*sqrt(2) = 16 + 16*sqrt(2). But how do you deduce the hypotenuse = 16 just from the algebra shown above? I'm still not following the logic...

Can anyone help?

since the perimeter is 16 + 16*(sqrt)2 and the triangle is isosceles we can say that either the hypotenuse is 16 or 16*(sqrt)2.
let us assume it is 16(sqrt)2 ... hence the other two sides should be 16/2 each .. which gives us 8.
as it is a right angle triangle, we can apply pythagoras theorem here .. which gives us the hypotenuse as 8(sqrt)2 ... which contradicts with the value of hypotenuse (16(sqrt)2) we already assumed in the beginning .. hence hypotenuse can't be 16(sqrt)2

apply the same method by taking hypotenuse as 16 and the other two sides as 8(sqrt)2 . this will provide the desired result.

Hope it helps

The perimeter of a certain isosceles right triangle is 16 +16√2. What is the length of the hypotenuse of the triangle?

A. 8
B. 16
C. 4√2
D. 8√2
E. 16√2

In an isosceles right triangle, the sides are proportioned s:s:s√2 so that h = s√2. Let's plug in the answer choices, which represent the length of h (the hypotenuse):

Answer choice C:
4√2 = s√2
s = 4
p = s+s+h = 4+4+4√2 = 8+4√2. Doesn't work.

Answer choice B:
16 = s√2
s = 16/√2 = (16√2)/√2*√2) = (16√2)/2 = 8√2
p = s+s+h = 8√2 + 8√2 + 16 = 16√2 + 16. Success!

The correct answer is B.