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 - Page 678: 39



Work Step by Step

The given triangle is an equilateral triangle. In an equilateral triangle the height bisects the base into two equal parts. Hence, a right triangle is formed where one of the legs is $5$ units and the hypotenuse is $10$ units. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ a=5 $ and $ c=10 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 5^2+b^2=10^2 \\\\ 25+b^2=100 \\\\ b^2=100-25 \\\\ b^2=75 \\\\ b=\sqrt{75} \\\\ b=\sqrt{25\cdot3} \\\\ b=\sqrt{(5)^2\cdot3} \\\\ b=5\sqrt{3} .\end{array} Hence, the missing side measures $ 5\sqrt{3} $ units.
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