PM is the median of ΔPQR . O is the centroid of ΔPQR. If PO = 27 cm. then what is the length of PM?

40.5 cm

The centroid of a triangle divides the medians into segments in the ratio of 2 : 1, where the centroid is closer to the midpoint of the side (where the median intersects the side).

Given that PO = 27 cm, if we let PM = X

\(\frac{2}{3}\) x X = 27

X = 27 x \(\frac{3}{2}\)

X = 40.5 cm

So, the length of PM is 40.5 cm.