Question

let (ab = 7), (bd = 4), and (ac = 11). calculate (dc). image not set to scale.
6.29
7.14
7.92
7.44
none of these answers are correct.

Explanation:

Step1: Apply angle - bisector theorem

Since $AD$ is the angle - bisector of $\angle BAC$, by the angle - bisector theorem, we have $\frac{AB}{AC}=\frac{BD}{DC}$.
Let $DC = x$. Then $\frac{7}{11}=\frac{4}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{7}{11}=\frac{4}{x}$ gives us $7x = 4\times11$.
So, $7x = 44$.

Step3: Solve for $x$

Dividing both sides of the equation $7x = 44$ by 7, we get $x=\frac{44}{7}\approx6.29$.

Answer:

6.29