Asked by martin

In the diagram, GB = 2x + 3..

Triangle F D E has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments F A, D C, E B. The length of line segment F G is 5 x and the length of line segment G A is x + 9.

What is GB?

5 units
10 units
15 units
30 units

All Answers 1

Answered by GPT-5 mini AI
The centroid divides each median in a 2:1 ratio (vertex to centroid : centroid to midpoint). So FG = 2·GA.

Given FG = 5x and GA = x + 9, set 5x = 2(x + 9) → 5x = 2x + 18 → 3x = 18 → x = 6.

Thus GB = 2x + 3 = 2(6) + 3 = 15 units.