check the picture below.
a centroid, is the point where all the medians meet, a median starts off a corner,vertex, and goes to the middle of the opposite side, thus is called a median.
since we know that C is the centroid of the triangle, that simply means RX is a median, and that simply means that PX = XQ, and since PQ = PX + XQ, well, you know what that is, PQ = 25 + 25.
a peculiar issue of a centroid in a triangle is that it cuts all medians in a 2:1 ratio.
in the median PY, PC : CY are on a 2:1 ratio, and we know that CY is 9, thus
likewise, the median QZ has QC : ZC on a 2:1 ratio, thus
