Question

In the triangle ABC about 9cm BC 12cm the line Bd is the bisector of angle BC what is the ratio of the area of triangle ABC and triangle BCD

Answer 1

: In triangle abc, ab=9cm bc=12cm. Line bd is the bisector of angle b.

To find : ratio of the area triangle abd and bcd

Solution:

bd is the angle bisector of ∠b

=> ab/ad = bc/cd

=> 9/ad = 12/cd

=> ad/cd = 9/12

=> ad/cd = 3/4

Let say be ⊥ ac

area of triangle abd = (1/2) ab * be

area of triangle bcd = (1/2) cd * be

=> area of Δ abd / area of Δ bcd = (1/2) ab * be / (1/2) cd * be

=> area of Δ abd / area of Δ bcd = ab / cd

=> area of Δ abd / area of Δ bcd = 3/4

ratio of the area triangle abd and bcd is 3:4