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?

1 Answer
Aug 19, 2016

36

Explanation:

drawn

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#