Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Common Core Cumulative Standards Review - Selected Response - Page 486: 18


$x = 3.75$

Work Step by Step

According to the side-splitter theorem, if a line is parallel to a side of a triangle and intersects the other two sides, then those two sides are divided proportionately. Let's set up a proportion for the sides whose values are given in the figure: $\frac{x}{5} = \frac{3}{4}$ Use the cross product property to get rid of the fractions: $4x = 5(3)$ Evaluate what is in parentheses first: $4x = 15$ Divide each side of the equation by $4$ to solve for $x$: $x = 3.75$
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