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: 12

Answer

$x=8$ in.

Work Step by Step

RECALL: Two triangles are similar if: (1) corresponding angles are congruent (2) corresponding sides are proportional (i) Notice that the three pairs of corresponding angles are congruent. (ii) Notice also that the two pairs of corresponding sides are proportional. Thus, the two triangles are similar. Solve for the missing length using ratios to obtain: $\dfrac{18}{12} = \dfrac{12}{x}$ Cross-multiply to obtain: $18x=12(12) \\18x=144 \\x = \frac{144}{18} \\x=8$ Therefore, the missing length is $8$ inches.
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