the centroid in a triangle is the point where all the "medians" meet.
the medians are of course the segments going from a vertex to the middle of the opposite side.
now, one thing about the centroid, it cuts all medians in a 2:1 ratio.
by looking at the graph, we can see that BP is the longer, so BP : PM are on a 2:1 ratio, thus
[tex]\bf \cfrac{BP}{PM}\implies \cfrac{7x+4}{2x+5}=\cfrac{2}{1}\implies 7x+4=4x+10
\\\\\\
3x=6\implies x=\cfrac{6}{3}\implies x=2\qquad \qquad \qquad\qquad \boxed{PM=2(2)+5}[/tex]
