Question

The perimeter of a certain isosceles right triangle is \small 16+16\sqrt{2} what is the length of the hypotenuse of the triangle?

Answer 1

If the hypotenuse of a 45°-45°-90° triangle is x, the legs are each x(√2)/2. Then the perimeter of the triangle is

... p = x + 2·x(√2)/2 = x + x√2

This matches your given perimeter with x=16.

The length of the hypotenuse is 16 units.