D is the centroid of △ABC. What is the value of x when GD=x+4 and GC=4x+5?

Question

Answer 1

The centroid is the intersection of the medians of a triangle

For each median, the distance from the vertex where the median starts is 2/3 of the distance to the opposite side, so the segment CD is 2/3 of the length of segment GC.

That would also mean that segment GD is 1/3 of the length of segment GC.

Translating that into an equation:

GD = GC/3

x + 4 = (4x + 5)/3

3x + 12 = 4x + 5

7 = x