## Intermediate Algebra (6th Edition)

$3\sqrt{5} \text{ } ft.$
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where the legs are given the measures $6$ feet and $3$ feet, then the hypotenuse, $c$, is equal to \begin{array}{l}\require{cancel} 6^2+3^2=c^2 \\\\ 36+9=c^2 \\\\ 45=c^2 \\\\ c=\sqrt{45} \\\\ c=\sqrt{9\cdot5} \\\\ c=\sqrt{(3)^2\cdot5} \\\\ c=3\sqrt{5} .\end{array} Hence, the unknown side is $3\sqrt{5} \text{ } ft.$