Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 253: 33


$UT=5\sqrt 5$

Work Step by Step

In $\triangle RST$ $RT^{2}=RS^{2}+ST^{2}$ $RT^{2}=6^{2}+8^{2}$ $RT^{2}=36+64$ $RT^{2}=100$ $RT=10$ now in $\triangle UTR$ $UT^{2}=RU^{2}-RT^{2}$ $UT^{2}=15^{2}-10^{2}$ $UT^{2}=225-100$ $UT^{2}=125$ $UT=\sqrt 125$ $UT=5\sqrt 5$
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