# If a=8 and b=6, how do you find c?

May 17, 2018

$c = 10$

#### Explanation:

If $a , b , c$ are the sides of a right triangle, and $c$ is the hypotenuse (the longest side), then the Pythagorean theorem states that:

$\textcolor{w h i t e}{m m m m m m m m m} \textcolor{b l u e}{\overline{\underline{|} {a}^{2} + {b}^{2} = {c}^{2} |}}$

So here, $a = 8 , b = 6$.

$\therefore {c}^{2} = {8}^{2} + {6}^{2}$

$= 64 + 36$

$= 100$

$c = \sqrt{100}$

$= \pm 10$

Since this is a length, we cannot take the negative side, as that'll make no sense! So, we only take the positive root, and the final answer is:

$c = 10$