# How do you find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12?

Apr 22, 2018

The length of the hypotenuse is $13$.

#### Explanation:

Using the Pythagorean theorem,

${a}^{2} + {b}^{2} = {c}^{2}$

where $c$ is the hypotenuse and $a$ and $b$ are the other two sides of a right triangle, we can solve for $c$:

${5}^{2} + {12}^{2} = {c}^{2}$

$25 + 144 = {c}^{2}$

$169 = {c}^{2}$

$\sqrt{169} = \sqrt{{c}^{2}}$

$\sqrt{169} = c$

$13 = c$