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: 13

Answer

$x=6$ meters

Work Step by Step

RECALL: Two triangles are similar if their corresponding angles are congruent. Having congruent corresponding angles means that similar triangles have corresponding sides that are proportional. The given triangles have two pairs of corresponding angles that are congruent. This means that the third pair of angles is also congruent. The corresponding side lengths are: 30 and 10; 18 and $x$. Solve for $x$ using ratio and proportion to obtain: $\dfrac{30}{10} = \dfrac{18}{x}$ Cross-multiply to obtain: $30(x) = 10(18) \\30x = 180 \\x = \frac{180}{30} \\x=6$ Thus, the missing length $x$ is 6 meters long.
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