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?
1 Answer
Mar 24, 2017
Explanation:
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#