There doesn't seem to be any reason why BG should be equal to CG.
If G is the centroid then BG = 2*GE (because and ). That will give you an equation for x.
From this picture,
Find the length of line DG.
Line AG= 13x-3
line BG= 4x + 3
line CG= 3x + 14
line EG= 11
I figured BG = CG, so I set them equal and got x= 11.
I plugged the x value into everything, reviewed the centriod theorem formulas (e.g. line AD = AG )