Question

Point d is the centroid of triangle abc use the given information to find x.

GD=2x-8 and GC=3x+3

Answer 1

The centroid D cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.

Therefore: |DC| = 2|GD|
|GC| = |GD| + |DC| = |GD| + 2|GD| = 3|GD|

so... we have:

3x + 3 = 3(2x-8)
3x + 3 = 3 × 2x - 3 × 8
3x + 3 = 6x - 24 |subtract 3 from both sides
3x = 6x -27 |subtract 6x from both sides
-3x = -27 |divide both sides by (-3)

x = 9

Answer 2

Answer and workings in the attachments below.

x=9.