Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 5 - Section 5.6 - Segments Divided Proportionally - Exercises - Page 268: 36

Answer

AD = 10; BD = 5

Work Step by Step

Using the book's recommendation to use AD = 2x and BD = x as well as the Pythagorean theorem, we have: $(2x)^2 - 6^2 = (x+3)^2 \\ 3x^2 - 6x - 45 = 0 \\ 3(x-5)(x+3) = 0 \\ x=5$ Thus: $AD =2(5) = 10 \\ BD = 5 $
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