## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set - Page 729: 57

#### Answer

$\sqrt{100.84} \text{ } mm \text{ OR } \approx 10.0 \text{ } mm$

#### 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 $c^2=a^2+b^2,$ with $a= 7$ and $b= 7.2 ,$ then \begin{array}{l}\require{cancel} c^2=7^2+7.2^2 \\\\ c^2=49+51.84 \\\\ c^2=100.84 .\end{array} Taking the principal square root of both sides (since there are no negative side measurement) results to \begin{array}{l}\require{cancel} c=\sqrt{100.84} .\end{array} Hence, the missing side is $\sqrt{100.84} \text{ } mm \text{ OR } \approx 10.0 \text{ } mm .$

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