Question

In ∆ABC, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Answer 1

We have to find the value of BD.

Given AB = 18cm ,AC= 15cm and  `BC = 22cm`.

In Δ ABC, AD the bisector of  `∠ A.`.

`(AB)/(AC)=(BD)/(DC)`

`(AB)/(AC)=(BD)/(BC-BD)`

`18/15=(BD)/(22-BD)`

On cross multiplication, we get

`6(22-BD)=5xxBD`

`132-6BD=5BD`

`132=5BD+6BD`

`132=11BD`

`BD=12cm`

Hence, the value of BD is  12 cm.