Question

segment bd bisects angle abc. solve for x. round to the nearest tenth, if necessary. (image not necessarily to scale)
triangle abc with point d on ac, ab = 18, ad = 9, dc = 8, bc = x, and bd as angle bisector

Explanation:

Step1: Apply Angle Bisector Theorem

$\frac{AB}{BC} = \frac{AD}{DC}$

Step2: Substitute known values

$\frac{18}{x} = \frac{9}{8}$

Step3: Cross-multiply to solve for x

$9x = 18 \times 8$
$9x = 144$
$x = \frac{144}{9}$

Answer:

16.0