hypotenus of an isoceles right triangle

When you transcribed the question, you missed an important part. I've posted the original question below.

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√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

susahntgupta402 wrote:Mitch and Brent is the reason for assuming right isosceles triangle occurrence of 2^1/2?

The question tells us that we have a right isosceles triangle.

Cheers,
Brent

Oops, sorry.
Looks like the person who posted the question transcribed it incorrectly.
The original question states that it's an isosceles right triangle.

I've since noted this in my response above.

Cheers,
Brent