A triangle has corners at points A, B, and C. Side AB has a length of #26 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #14 #, what is the length of side BC?

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Answer 1 · 2017-11-20T11:56:53

Length of the side #BC# is #13.85# unit

Sides of triangle are #AB=26 , AC=14 , BC= ?#

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

#BD=9#. By the Angle Bisector Theorem we know,

#(BD)/(DC)=(AB)/(AC) or 9/(DC)=26/14 or DC=(14*9)/26#or

#DC=(7*9)/13=63/13 ~~4.85 :. BC=BD+DC=9+4.85#

#:. BC~~13.85# unit .

Length of the side #BC# is #13.85# unit [Ans]