A triangle has corners at points A, B, and C. Side AB has a length of #42 #. The distance between the intersection of point A's angle bisector with side BC and point B is #16 #. If side AC has a length of #32 #, what is the length of side BC?

Question

1317 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-11T12:06:40

#~~28.19#

Let #"M"# be the point of intersection of the angle bisector of #"A"#

enter image source here

We need to find the length of #"BC"#

#color(blue)(("BM")/("CM")=("AB")/("AC")#

So,

#rarr16/("MC")=42/32#

#rarr16/("MC")=21/16#

Cross multiply

#rarr"MC"*21=16*16#

#rarr"MC"*21=256#

#rarr"MC"=256/21#

#rArr"MC"~~12.19#

So the length of #"BC"# will be #"BM"+"CM"=16+12.19=color(PURPLE)(28.19#