Question

In triangle abc, ab=9cm bc=12cm. Line bd is the bisector of angle b. What is the ratio of the area triangle abd and bcd

Answer 1

Given : 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

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Answer 2

Answer:

In the triangle ABC AB =9cm BC =12cm. The line BD is the bisector of Angle B what is the ratio of area of triangle ABC and triangle BCD