The centroid (the point where the medians meet) divide each median into parts with lengths in a ratio of 2:1. This means 7x + 1 is twice the length of 3x + 4, or
7x + 1 = 2 (3x + 4)
Solve for x :
7x + 1 = 6x + 8
7x - 6x = 8 - 1
x = 7
Then XE has length
XE = 4•7 - 2 = 28 - 2 = 26
FX is twice this length, so
FX = 2•26 = 52
and so FE has length
FE = FX + XE = 52 + 26 = 78
