A triangle has corners at points A, B, and C. Side AB has a length of #44 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #32 #, what is the length of side BC?

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Answer 1 · 2016-06-24T10:35:54

#(BC)=24*76/44=24*19/11~=41.45.#

Suppose that the bisector of #/_A# meets side #BC# in #D.#

So, from what is given, we conclude that in #DeltaABC#, #AB=44, AC=32, BD=24.#

Now, by the property of #/_# bisector, we have, #(AB)/(AC)=(BD)/(DC).#

Using, reverse compodundo, #(AB)/(AB+AC)=(BD)/(BD+DC)=(BD)/( BC).#

Subbing the above values, #44/(44+32)=24/(BC),# or, #(BC)=24*76/44=24*19/11~=41.45.#