The length of the segment DG is 34 units
How to determine the length DG?
The attached figure represents the missing information in the question
The point G is the centroid of the triangle.
This means that:
CG : DG = 1 : 2
Express as fraction
CG/DG = 1/2
Multiply both sides by 2
DG = 2 * CG
Substitute the given parameters:
3x - 2 = 2 *(x + 5)
Expand
3x - 2 = 2x + 10
Evaluate the like terms
x = 12
Recall that:
DG = 3x - 2
So, we have:
DG = 3 * 12 - 2
Evaluate
DG = 34
Hence, the length DG is 34 units
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