# How do you solve for the missing side, c, of a right triangle if a=12 and b=16?

Mar 3, 2018

See a solution process below:

#### Explanation:

The Pythagorean Theorem states, for a right triangle:

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

Where:

• $c$ is the hypotenuse of the right triangle

• $a$ and $b$ are the legs of the right triangle

Substituting and solving for $c$ gives:

${c}^{2} = {12}^{2} + {16}^{2}$

${c}^{2} = 144 + 256$

${c}^{2} = 400$

$\sqrt{{c}^{2}} = \sqrt{400}$

$c = 20$