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A triangle has corners at points A, B, and C. Side AB has a length of #45 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #36 #, what is the length of side BC?

Answer 1

Evelyn Arboleda

#21 3/5" units"#

Let D be the point on BC where the angle bisector intersects BC.

#"Then " BC= BD+DC#

#"We know " BD=12" and have to find " DC#

Using the #color(blue)"Angle bisector theorem"" on the triangle"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))#

Substitute given values into the equation.

#rArr45/36=12/(DC)#

#color(blue)"cross multiply"#

#rArr45DC=12xx36#

#rArrDC=(12xx36)/45=48/5=9 3/5#

#rArrBC=12+9 3/5=21 3/5#

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Answer 2

Allison Allen

Side BC has a length of 27.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.