A triangle has corners at points A, B, and C. Side AB has a length of #16 #. 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 #27 #, what is the length of side BC?
1 Answer
Mar 14, 2017
Explanation:
Let D be the point on BC where the angle bisector from A, intersects BC
#rArrBC=BD+DC# We know BD = 12 and require to find DC
Applying the
#color(blue)"Angle bisector theorem"# to the triangle.
#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))# Substitute known values into the equation.
#rArr16/27=12/(DC)#
#color(blue)"cross multiply"#
#rArr16DC=12xx27#
#rArrDC=(12xx27)/16=20 1/4#
#rArrBC=12+20 1/4=32 1/4" units"#