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A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #24 #, what is the length of side BC?

Answer 1

Sophia Alfred

15 units

Firstly , let the point where the angle bisector intersects with side BC be D.

Then by the #color(blue)" Angle bisector theorem " #

#( BD)/(DC) = (AB)/(AC) ", DC is required to be found "#

substitute in the appropriate values into the ratios to obtain:

# 7/(DC) = 21/24 rArr 21DC = 7xx24rArr DC = (7xx24)/21 = 8#

now BC = BD + DC = 7 + 8 = 15 units

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