A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #16 #, what is the length of side BC?
1 Answer
May 3, 2016
10
Explanation:
Here is a sketch (not to scale)
To calculate BC we require the length of DC.
Using the
#color(blue)" Angle bisector theorem "#
#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.
hence
#6/(DC)=24/16# now cross-multiply
#rArr 24xxDC=16xx6rArr DC=(16xx6)/24=4# Now BC = BD + DC = 6 + 4 = 10
