Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set: 51


$3\sqrt{5} \text{ } ft.$

Work Step by Step

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. $
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