Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set: 9

Answer

$c=9\sqrt{2} \\\\ c\approx12.728 $

Work Step by Step

In the given right triangle, $a$ and $b$ are the legs and $c$ is the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ a=9 $ and $ b=9 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 9^2+9^2=c^2 \\\\ 81+81=c^2 \\\\ 162=c^2 \\\\ c=\sqrt{162} \\\\ c=\sqrt{81\cdot2} \\\\ c=\sqrt{(9)^2\cdot2} \\\\ c=9\sqrt{2} \\\\ c\approx12.728 .\end{array}
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