A triangle has corners at points A, B, and C. Side AB has a length of #12 #. 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 #9 #, what is the length of side BC?

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Answer 1 · 2017-11-21T11:11:14

Length of the side #BC# is #5.25# unit.

Sides of triangle are #AB=12 , AC=9 , BC= ?#

Let the angle bisector of #/_A#, AD meets BC at D.

#BD=3#. By the Angle Bisector Theorem we know,

#(BD)/(DC)=(AB)/(AC) or 3/(DC)=12/9 or DC=(3*9)/12#or

#DC=9/4 =2.25 :. BC=BD+DC=3+2.25=5.25#

#:. BC=5.25# unit .

Length of the side #BC# is #5.25# unit [Ans]