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: 20


$x = 4.8$

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: $\frac{3}{x} = \frac{5}{8}$ Use the cross product property to get rid of the fractions: $5x = 24$ Divide each side of the equation by $5$ to solve for $x$: $x = 4.8$
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