Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - Chapter Review - Page 482: 26


$x = 12$

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: $\frac{x - 3}{x} = \frac{12}{16}$ Use the cross product property to get rid of the fractions: $12x = 16(x - 3)$ Evaluate what is in parentheses first: $12x = 16x - 48$ Subtract $16x$ from each side to move variables to one side of the equation: $-4x = -48$ Divide each side of the equation by $-4$ to solve for $x$: $x = 12$
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