in tri.ABC, altitude AD=18 ,median BE =9√5 and median CF=15. find BC(plzz xplain)

Hello student,
Please find the answer to your question below
LetGthe centroid of△ABC,GHthe height of△GBCrelative toBCandFKthe height of△FBCrelative toBC. Recall that:
CG=2/3CF=10and
BG=2/3BE=6√5.
Note that△BFK∼△BADand that△CGH∼△CFK, hence:
FK=1/2AD=9and
GH=2/3FK=6.
Using Pytagoras we get:
BH=12andHC=8.
Therefore BC=20.