Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 23 Page 482

7.5

Practice makes perfect

Let's analyze the given figure.

Since we are given a triangle with a segment that is bisecting one of the angles, we can use the Triangle-Angle-Bisector Theorem.
This theorem tells us that the two segments opposite the bisected angle are proportional to the two other sides of the triangle. We are given the expressions for the lengths of these sides and segments, so we can write a proportion. x/7 = 15/14 Let's solve it using the Cross Product Property.
x/7 = 15/14
14x = 7*15
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Solve for x
14x = 105
x = 105/14
x=7.5