In the adjoining figure, AD is bisector of ∠BAC. If AB = 6 cm, AC = 4 cm and BD = 3 cm, find BC.

We know that,

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

$\therefore \dfrac{BD}{DC} = \dfrac{AB}{AC}$.

Putting values in above equation we get,

$\Rightarrow \dfrac{3}{DC} = \dfrac{6}{4} \\[1em] \Rightarrow DC = \dfrac{3 \times 4}{6} \\[1em] \Rightarrow DC = \dfrac{12}{6} \\[1em] \Rightarrow DC = 2 \text{ cm}.$

BC = BD + DC = 3 + 2 = 5 cm.

Hence, the length of BC = 5 cm.