A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #15 #, what is the length of side BC?

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Answer 1 · 2017-05-21T04:40:00

#BC=16# units

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According to angle bisector theorem,
#(AB)/(AC)=(BD)/(DC)#
Given #AB=9, AC=15 and BD=6#,
#=> 9/15=6/(DC)#

#=> DC=(6xx15)/9=10#

Hence, #BC=BD+DC=6+10=16# units