## Intermediate Algebra (12th Edition)

$c=13$
According to the Pythagorean Theorem, if $a$ and $b$ are the lengths of the shorter sides of a right triangle and $c$ is the length of the longest side, then $a^{2}+b^{2}=c^{2}$. Therefore, $5^{2}+12^{2}=c^{2}$. $25+144=c^{2}$ $169=c^{2}$ Take the square root of both sides. $\sqrt 169=c=13$ (where we know that $c$ must be positive, since it is a length)