Question

In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.

Triangle D E F has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments D C, E B, F A.

[Figure may not be drawn to sacle]

What is DG?

12 units
17 units
34 units
51 units

Answer 1

The centroid divides each median in a 2:1 ratio (vertex to centroid : centroid to midpoint = 2:1). So DG = 2·CG.

Set 3x − 2 = 2(x + 5):
3x − 2 = 2x + 10 → x = 12.

Then DG = 3x − 2 = 3(12) − 2 = 34 units.