# Using the Pythagorean Theorem, how do you find the length of side a given that side c=40 and b=20?

Mar 20, 2018

$20 \sqrt{3}$

#### Explanation:

assuming $c$ is the hypotenuse we have

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

$\therefore {a}^{2} + {20}^{2} = {40}^{2}$

$\implies {a}^{2} = {40}^{2} - {20}^{2}$

${a}^{2} = \left(40 + 20\right) \left(4 - 20\right) = 60 \times 20 = 1200$

$a = \sqrt{1200} = 20 \sqrt{3}$