A triangle has corners at points A, B, and C. Side AB has a length of #32 #. The distance between the intersection of point A's angle bisector with side BC and point B is #16 #. If side AC has a length of #28 #, what is the length of side BC?

1 Answer
Apr 3, 2016

30

Explanation:

Firstly , let the point where the angle bisector intersects with side BC be D.

Then by the #color(blue)" Angle bisector theorem " #

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

Require to find DC.

Substitute the appropriate values into the ratio to obtain.

#(16)/(DC) = 32/28 #

now cross-multiply : #32xxDC = 28xx16 #

To obtain DC , divide both sides by 32

#( cancel(32) DC)/cancel(32) = (28xx16)/32 #

# rArr DC = 14 #

Now , BC = BD + DC = 16 + 14 = 30