Question

In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. If BD = 2 cm, AB = 5 cm, and DC = 3 cm, find AC.

Answer 1

Given: Δ ABC and AD bisects ∠A, meeting side BC at D. And BD = 2 cm, AB = 5 cm, and DC = 3 cm. 

Required to find: AC

Since, AD is the bisector of ∠ A meeting side BC at D in Δ ABC

⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\) 

\(\frac{5}{AC}\) = \(\frac{2}{3}\) 

2AC = 5 x 3 

∴ AC = 7.5 cm