Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set - Page 729: 55


$2\sqrt{131} \text{ } m \text{ OR } \approx 22.9 \text{ } m$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Pythagorean Theorem to solve for the value of the missing side measurement. $\bf{\text{Solution Details:}}$ Based on the given figure, the missing side is one of the legs of the right triangle. Let $a$ be the missing side measurement. Using the Pythagorean Theorem which is given by $a^2+b^2=c^2,$ with $b= 9 $ and $c= 11\sqrt{5} ,$ then \begin{array}{l}\require{cancel} a^2+9^2=(11\sqrt{5})^2 \\\\ a^2+81=121(5) \\\\ a^2+81=605 \\\\ a^2=605-81 \\\\ a^2=524 .\end{array} Taking the principal square root of both sides (since there are no negative side measurement) and simplifying the radical result to \begin{array}{l}\require{cancel} a=\sqrt{524} \\\\ a=\sqrt{4\cdot131} \\\\ a=\sqrt{(2)^2\cdot131} \\\\ a=2\sqrt{131} .\end{array} Hence, the missing side is $ 2\sqrt{131} \text{ } m \text{ OR } \approx 22.9 \text{ } m .$
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