Question

question
segment (overline{bd}) bisects (angle abc). solve for (x). round to the nearest tenth, if necessary. (image not necessarily to scale.)
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attempt 1 out of 2
(x=)
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Explanation:

Step1: Apply the Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, $\frac{AB}{BC} = \frac{AD}{DC}$.
Given $AB = x$, $BC = 18$, $AD = 15$, $DC = 13$. So, $\frac{x}{18} = \frac{15}{13}$.

Step2: Solve for \( x \)

Cross - multiply to get $13x = 18\times15$.
Calculate $18\times15 = 270$. Then, $x=\frac{270}{13}\approx20.8$.

Answer:

\( 20.8 \)