Given AF FB AD 24 GE 5 CG 14 Find AG BG FG SolutionBy wha

Given: AF FB AD = 24 GE = 5 CG = 14 Find: AG, BG, FG

Solution

By what is given AD bisects BC, BE bisects AC and CF bisects AB. Therefore AD, BE and CF are medians, and point G is the Centroid. The centrods property is that it divides each median in the ratio 2:1.

Therefore AG/GD = BG/GE = CG/GF = 2/1

AG/GD = 2/1. Given AD = 24, Therefore AG = (2/3) * 24 = 16

Given GE = 5 and BG/GE = 2/1. Therefore BG = 5 * 2 = 10

Given CG = 14 and CG/GF = 2/1. Therefore GF = CG/2 = 14/2 = 7.