GeminiHeat wrote:
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√2Now 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 = 16Answer = B
Cheers,
Brent