# The length of a leg of an isosceles right triangle is 5sqrt2 units. What is the length of the hypotenuse?

Mar 27, 2018

hypotenuse = 10

#### Explanation:

You are given the leg length of one side, so you are basically given both leg lengths because an isosceles right triangle has two equal leg lengths:

$5 \sqrt{2}$

In order to find the hypotenuse you need to do
${a}^{2} + {b}^{2} = {c}^{2}$

$a$ = leg length 1
$b$ = leg length 2
$c$ = hypotenuse

${\left(5 \sqrt{2}\right)}^{2} + {\left(5 \sqrt{2}\right)}^{2} = {c}^{2}$
$\left(25 \cdot 2\right) + \left(25 \cdot 2\right) = {c}^{2}$
$50 + 50 = {c}^{2}$
$100 = {c}^{2}$
$\sqrt{100} = \sqrt{{c}^{2}}$
$10 = c$
hypotenuse = 10