Question

F

F
A
B
units
G is the centroid of triangle ABC.
What is the value of x?
What is the length of segment DG?
What is the length of segment AG?
What is the length of segment AD?
x + 2
units
units
X-15
G
G
D
E
C
с

Answer 1

• x = 37
• DG = 22
• AG = 44
• AD = 66

Explanation:

We presume your "centroid ratio theorem" tells you that AG = 2·DG, so ...

(x+7) = 2(x -15)

x + 7 = 2x - 30 . . . . eliminate parentheses

37 = x . . . . . . . . . . .add 30-x

Then AG = 37+7 = 44

and DG = 37-15 = 22.

Thus, AD = AG +GD = 44 +22 = 66