A triangle has corners at points A, B, and C. Side AB has a length of 32 32. The distance between the intersection of point A's angle bisector with side BC and point B is 16 16. If side AC has a length of 28 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 " Angle bisector theorem
( BD)/(DC )= (AB)/(AC) BDDC=ABAC Require to find DC.
Substitute the appropriate values into the ratio to obtain.
(16)/(DC) = 32/28 16DC=3228 now cross-multiply :
32xxDC = 28xx16 32×DC=28×16 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
