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 #8 #. If side AC has a length of #35 #, what is the length of side BC?

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Answer 1 · 2016-09-16T15:10:24

#19.7#

Let's draw a neat diagram

enter image source here

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

#color(blue)(("AB")/("BD")=("AC")/("DC")#

#:.rarr24/8=35/("DC")#

#rarr3=35/("DC")#

#rarr3("DC")=35#

#rArr# #color(green)("DC"=35/3~~11.7#

#:."The total length of BC=(BD)+(DC)"#

#color(green)(rArr8+11.7=19.7#