## Intermediate Algebra (12th Edition)

$b=3\sqrt 5$
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, $6^{2}+b^{2}=9^{2}$. $36+b^{2}=81$ Subtract 36 from both sides. $b^{2}=45$ Take the square root of both sides. $b=\sqrt 45=\sqrt (9\times5)=\sqrt 9\times\sqrt5=3\sqrt 5$