A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #15 #. If side AC has a length of #27 #, what is the length of side BC?
1 Answer
May 22, 2016
26.25
Explanation:
Here is a sketch (not to scale)
To calculate the length of BC , we require the length of DC.
Using the
#color(blue)"Angle bisector theorem"# For the triangle ABC given, this is.
#color(red)(|bar(ul(color(white)(a/a)color(black)((BD)/(DC)=(AB)/(AC))color(white)(a/a)|)))# Substitute the appropriate values into the ratio.
#rArr15/(DC)=36/27# now cross-multiply
#rArrDCxx36=15xx27rArrDC=(15xx27)/36# Thus DC
#=45/4=11 1/4=11.25# length of BC = BD + DC = 15 + 11.25 = 26.25
