Question

Point G is the centroid of triangle ABC. Use the given information to find the value of x?
18. CG = 3X + 7 and CE = 6x
19. FG= x+8 and AF = 9x-6
20. BG= 5X-1 and DG = 4X-5
please find it in each situation

Answer 1

Because G is the centroid of the triangle ABC, then AG = BG= CG
here CG = 3x+7 and BG= 6x
3x+7 = 6x
3x = 7
x = 7/3

Answer 2

For the question to be "workable", AF is probably the median, with F on BC

remember the centroid cuts the median in the ratio of 2:1, or AG:GF = 2:1
then FG:AF = 1:3
(x+8)/(9x-6) = 1/3
9x - 6 = 3x + 24
6x = 30
x = 5