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: 56

Answer

$5\sqrt{7} \text{ } cm \text{ OR } \approx 13.2 \text{ } cm$

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 the hypotenuse, $c,$ of the right triangle. Using the Pythagorean Theorem which is given by $c^=a^2+b^2,$ with $a= 5\sqrt{3} $ and $b= 10 ,$ then \begin{array}{l}\require{cancel} c^2=(5\sqrt{3})^2+10^2 \\\\ c^2=25(3)+100 \\\\ c^2=75+100 \\\\ c^2=175 .\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} c=\sqrt{175} \\\\ c=\sqrt{25\cdot7} \\\\ c=\sqrt{(5)^2\cdot7} \\\\ c=5\sqrt{7} .\end{array} Hence, the missing side is $ 5\sqrt{7} \text{ } cm \text{ OR } \approx 13.2 \text{ } cm .$
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