Question

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

Answer 1

Answer:

$5\sqrt{10}\ in$

Step-by-step 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

$(10\sqrt{5})^2=a^2+a^2$

solve for a

$500=2a^2$

Divide by 2 both sides

$a^2=250$

$a=\sqrt{250}\ in$

Simplify

$a=5\sqrt{10}\ in$