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