A triangle has corners points A, B, and C. Side AB has a length of #5 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #4 #, what is the length of side BC?

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Answer 1 · 2017-12-21T09:54:43

Length of side BC = 5.4

Let the point where the angle bisector intersects with
side BC be D

#"using the "color(blue)"angle bisector theorem"#

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

#5 / 4 = 3 / (DC)#

#DC = (3*4) / 5 = 2.4#

#BC = BD+DC= 3+2.4 =5.4#