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 5.1 - Ratios, Rates, and Proportions - Exercises - Page 229: 43

Answer

We must prove that the triangles are not similar triangles to solve this problem.

Work Step by Step

To prove the triangles are not similar, we first find the value of $a$ if the triangles were similar. In problem 42, we found that this would mean: $$ a=5$$ So, we find: $$ BD\cdot CD \ne BE \cdot AC \\ (5)(5)\ne (9)(6) \\ 25\ne 54$$ Thus, we see that the triangles are not similar, so the given expression is not true.
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