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 5.2 - Similar Polygons - Exercises - Page 236: 21



Work Step by Step

Since ADE ~ ABC we can assume that AE = AC and DE = CB. We are also told that CE = CB. We can call this X. Then we set up a proportion AE/AC = DE/BC. However we do not know the measure of AC or BC. We plug in 6 + X for AC and X for BC. The resulting proportion is 6/(6+X) = 4/X. Solve and the answer is BC = 12.
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