Applying the centroid ratio theorem, we have:
x = 37
DG = 22
AG = 44
AD = 66.
What is the Centroid Ratio Theorem?
According to the centroid ratio theorem, we have:
AG = 2/3(AD)
AG = x + 7
DG = x - 15
AD = x + 7 + x - 15 = 2x - 8
Plug in the values into the equation
x + 7 = 2/3(2x - 8)
3(x + 7) = 2(2x - 8)
3x + 21 = 4x - 16
3x - 4x = -21 - 16
-x = -37
x = 37
DG = x - 15 = 37 - 15 = 22
AG = x + 7 = 37 + 7 = 44
AD = 22 + 44 = 66
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