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: 42

Answer

$13\sqrt{2}$

Work Step by Step

The diagonal and the two sides of the square form a right triangle with the legs equal to $13.$ Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ a=13 $ and $ b=13 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 13^2+13^2=c^2 \\\\ 169+169=c^2 \\\\ c=\sqrt{169+169} \\\\ c=\sqrt{169(2)} \\\\ c=\sqrt{(13)^2\cdot2} \\\\ c=13\sqrt{2} .\end{array} Hence, the missing side measures $ 13\sqrt{2} $ units.
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