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 #8 #. If side AC has a length of #18 #, what is the length of side BC?

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Answer 1 · 2017-12-19T14:26:46

14 units.

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

So, According to this theorem,

#(AB)/(AC) = (BD)/(DC)# [Let the point of intersection of angle A's bisector with side BC be D.]

Putting the corresponding values in the relation we get,

#(24)/(18) = (8)/(DC)#

#rArr DC = (18 * 8)/24# units = #6# units

That means, #BC = BD + DC = (8 + 6)# units #= 14# units.