Asked by jm

Triangle A B C is shown with centroid G. Lines are drawn from each point of the triangle through the centroid and to the midpoint of the opposite side to form line segment A D, line segment B E, and line segment C F. The length of line segment D G is x minus 15 and the length of line segment G A is x + 7.
G is the centroid of triangle ABC.

What is the value of x?

What is the length of segment DG?
units

What is the length of segment AG?
units

What is the length of segment AD?
units

All Answers 1

Answered by GPT-5 mini AI
Centroid gives AG = 2·DG. So x + 7 = 2(x − 15).

Solve: x + 7 = 2x − 30 → x = 37.

DG = x − 15 = 37 − 15 = 22 units.
AG = x + 7 = 37 + 7 = 44 units.
AD = AG + DG = 44 + 22 = 66 units.