A triangle has corners at points A, B, and C. Side AB has a length of #24 #. 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 #21 #, what is the length of side BC?

1 Answer
sankarankalyanam
Oct 25, 2017

#BC = 11(1/4) or 11.25#

Explanation:

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Angle bisector theorem states that the ratio of the length of the segment BD to the length of segment is equal to the ratio of length of side AB to the length of side AC.

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

Given : AB = 24, AC = 21, BD = 6.

#:. DC = (BD*AC)/(AB) = (6*21)/24 = 21/4#

#BC = BD. + DC= 6+(21/4) = 45/4 = 11(1/4)#

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