Question

In a ∆ABC, it is given that AD is the internal bisector of ∠A. If BD = 4 cm, DC = 5 cm and AB = 6 cm, then AC = ?


(a) 4.5 cm
(b) 8 cm
(c) 9 cm
(d) 7.5 cm

Answer 1

(d) 7.5 cm
It is given that AD bisects angle A.
Therefore, applying angle bisector theorem, we get:

$$\begin{gathered} \frac{BD}{DC}=\frac{AB}{AC} \\ \Rightarrow \frac{4}{5}=\frac{6}{x} \\ \Rightarrow x=\frac{5\times 6}{4}=7.5 \end{gathered}$$

Hence, AC = 7.5 cm