Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - 7-5 Proportions in Triangles - Lesson Check - Page 474: 4


$x = 5$

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: $\frac{x}{10} = \frac{45 - 30}{30}$ Use the cross product property to get rid of the fractions: $30x = 10(45 - 30)$ Evaluate what is in parentheses first: $30x = 10(15)$ Multiply to simplify: $30x = 150$ Divide each side of the equation by $30$ to solve for $x$: $x = 5$
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