Question

segment \overline{bd} bisects \angle abc. solve for x. round to the nearest tenth, if necessary. (image not necessarily to scale.)

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, we have the proportion \(\frac{AD}{DC}=\frac{AB}{BC}\).

Step2: Substitute the known values into the proportion

We know that \(AD = 14\), \(DC=11\), \(BC = 12\), and \(AB=x\). Substituting these values into the proportion \(\frac{14}{11}=\frac{x}{12}\).

Step3: Solve for \(x\)

Cross - multiply to get \(11x=14\times12\). Then \(11x = 168\). Divide both sides by 11: \(x=\frac{168}{11}\approx15.3\).

Answer:

\(x\approx15.3\)