Question

In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. If AB = 5.6 cm, AC = 6 cm, and DC = 3 cm, find BC.

Answer 1

Given: Δ ABC and AD bisects ∠A, meeting side BC at D. And AB = 5.6 cm, AC = 6 cm, and DC = 3 cm. 

Required to find: BC

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

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

\(\frac{5.6}{6}\) = \(\frac{BD}{3}\) 

BD = \(\frac{5.6}{2}\) = 2.8 cm 

And, we know that, 

BD = BC – DC 

2.8 = BC – 3 

∴ BC = 5.8 cm