Question

The hypotenuse of a 45-45-90 has a length of 10

Answer 1

The length of one of its legs is
`5√(2)\ units`

Explanation:

The question is

What is the length of one of its legs?

we know that

An isosceles triangle has two equal sides and two equal interior angles

In this problem we have an isosceles triangle

Let

x ----> the measure of one of its legs

Applying the Pythagorean Theorem

`10^2=x^2+x^2`

solve for x

`100=2x^2`

Divide by 2 both sides

`50=x^2`

square root both sides

`x=√(50)\ units`

simplify

`x=5√(2)\ units`