The centroid is the point of concurrency of the medians of a triangle. In the given diagram, M is the centroid.
Using the Concurrency of Medians Theorem, we can write an equation that we can use to find the desired lengths, MB.
MB = 2/3RB
With the Segment Addition Postulate we can rewrite RB as the sum of the two smaller segments.
Additionally we are given that RM= 4, which we can substitute into the new equation.
RB = RM+MB ⇒ RB = 4+MB
Next, we can substitute the above expression into the initial equation and find the desired length.
