If in triangle ABC, D is a point on the side BC such that the line joining AD bisects the angle A. If the length of BD and BC are 4cm and 10cm respectively, then find the ratio of the lengths of AB and AC.

2 : 3

DC = BC - BD = 10 - 4 = 6 cm

According to the concept,

Since AD is the angle bisector of \(\angle\)BAC, AB : AC = BD : DC

So, AB : AC

= 4 : 6 = 2 : 3

Therefore, the ratio of the lengths of AB and AC is 2 : 3.