VJesus12 wrote: ↑Thu Apr 15, 2021 12:01 pm
The perimeter of a certain isosceles right triangle is \(16+16\sqrt2.\) What is the length of the hypotenuse of the triangle?
(A) \(8\)
(B) \(16\)
(C) \(4\sqrt2\)
(D) \(8\sqrt2\)
(E) \(16\sqrt2\)
Answer:
B
Source: GMAT Prep
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√2
From 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
