Find the value of x

Question

1. 

Answer 1

G is the centroid of the triangle and 2/3 of the distance from the vertex at B to the midpoint of CD at point B.

Since BG is 2/3 of the distance from B to D, so BG is 2/3 of BD.

BG = 2/3 * BD

x + 3 = 2/3 (4x - 18)

3x + 9 = 2 (4x - 18)

3x + 9 = 8x - 36

45 = 5x

x = 9