## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 7 - Similarity - Chapter Review - Page 482: 23

#### Answer

$x = 7.5$

#### Work Step by Step

According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle. Let's set up a proportion that compares the segments of the intersected side to the other two sides: $\frac{15}{14} = \frac{x}{7}$ Use the cross product property to get rid of the fractions: $14x = 15(7)$ Multiply to simplify: $14x = 105$ Divide each side of the equation by $14$ to solve for $x$: $x = 7.5$

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