**Quote:**

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

An IMPORTANT point to remember is that, in

any isosceles right triangle, the sides have length x, x, and x√2 for some positive value of x.

Note:

x√2 is the length of the hypotenuse, so our goal is to find the value of

x√2From here, we can see that the perimeter will be x + x +

x√2 In the question, the perimeter is 16 + 16√2, so we can create the following equation:

x + x +

x√2 = 16 + 16√2,

Simplify: 2x +

x√2 = 16 + 16√2

IMPORTANT: Factor

x√2 from the left side to get :

x√2(√2 + 1) = 16 + 16√2

Now factor 16 from the right side to get:

x√2(√2 + 1) = 16(1 + √2)

Divide both sides by (1 + √2) to get:

x√2 = 16

Answer = B

Cheers,

Brent

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