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 - Practice and Problem-Solving Exercises - Page 475: 11


$x = 10$

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: $\frac{x + 5}{x} = \frac{12}{8}$ Use the cross product property to get rid of the fractions: $8(x + 5) = 12x$ Use the distributive property first: $8x + 40 = 12x$ Subtract $8x$ from both sides of the equation to move variables to one side of the equation: $4x = 40$ Divide each side of the equation by $4$ to solve for $x$: $x = 10$
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