# Using the pythagorean theorem, how do you solve for the missing side given a = 10 and b = 20?

Mar 11, 2018

See a solution process below:

#### Explanation:

The Pythagorean Theorem states, for a right triangle:

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

Substituting for $a$ and $b$ and solving for $c$ gives:

${c}^{2} = {10}^{2} + {20}^{2}$

${c}^{2} = 100 + 400$

${c}^{2} = 500$

$\sqrt{{c}^{2}} = \sqrt{500}$

$c = \sqrt{100 \cdot 5}$

$c = \sqrt{100} \sqrt{5}$

$c = 10 \sqrt{5}$