Question

The hypotenuse of a 45 degrees -45 degrees -90 degrees triangle measures 10 root of 5 in.

Edited... Answer 5 root of 10

Answer 1

`5√(10)\ in`

Explanation:

The question is

Find the measure of the legs

we know that

In a 45 degrees -45 degrees -90 degrees triangle, the measure of the legs are equal

Let

a ----> the measure of one leg

Applying the Pythagorean Theorem

`(10√(5))^2=a^2+a^2`

solve for a

`500=2a^2`

Divide by 2 both sides

`a^2=250`

`a=√(250)\ in`

Simplify

`a=5√(10)\ in`