Find the length of a leg of an isosceles right triangle whose hypotenuse has a length of 8√2.

Answer 1

An isosceles right triangle is one with congruent legs. If we call the length of this triangle's leg a, and knowing the hypotenuse has length 8√2, the Pythagorean theorem relates these lengths by the relationship

a² + a² = (8√2)²

We can simplify this expression and solve for a:

2a² = (8√2)²

√2a = 8√2

a = 8

Answer 2

For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.