Question

In a ΔABC, AD is the bisector of ∠A, meeting side BC at D.

If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

Answer 1

In ΔABC, AD is the bisector of ∠A.

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"BD"/"DC"="AB"/"AC"`

`rArr"BD"/2.8=3.5/4.2`

`=(3.5xx2)/3`

`=7/3=2.33 ` cm

∴ 𝐵𝐷 = 2.3 cm