Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.2 Triangles - Exercise Set 10.2 - Page 627: 17

Answer

The length of the side CA is \[5\].

Work Step by Step

\[\Delta ABC\] and \[\Delta ADE\]are similar where, BA \[=\] 3, CB \[=\] 3 in\[\Delta ABC\] and ED \[=\] 9, EA \[=\] 15 in \[\Delta ADE\]. Thus, \[\frac{ED}{CB}=\frac{EA}{CA}\] Compute the value of side CA as shown below: \[\begin{align} & \frac{9}{3}=\frac{15}{CA} \\ & 9\times CA=15\times 3 \\ & 9CA=45 \\ & CA=5 \end{align}\] Hence, the length of the side CA is \[5\].
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