Based on the centroid theorem, the value of x is: 2.5.
What is the Centroid Theorem?
The centroid theorem states that, the centroid of a triangle equals two-third of the distance from each midpoint of a triangle to each vertex.
Given:
BD = 4x + 5
BF = 9x
Thus:
BD = 2/3(BF)
4x + 5 = 2/3(9x)
4x + 5 = 6x
4x - 6x = -5
-2x = -5
x = 5/2
x = 2.5
Therefore, based on the centroid theorem, the value of x is: 2.5.
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