Question

A triangle has corners at points A, B, and C. Side AB has a length of `48`. The distance between the intersection of point A's angle bisector with side BC and point B is `24`. If side AC has a length of `24`, what is the length of side BC?

Answer 1

36

Explanation:

In the figure

`"In "Delta ABC, AB=48 and AC= 24, AD" is the bisector of "/_CAD , BD=24`

Now By Angle Bisector Theorem we Know that Angle bisectors in a triangle have a characteristic property of dividing the opposite side in the ratio of the adjacent sides.

Let CD = x then

`(CD)/(BD)=(AC)/(AB)=>x/24=24/48=1/2=>x=24/2=12`

`:.CD=12`

Now `BC=BD+Cd=24+12=36`