Explanation:

- In an equilateral triangle, the centroid, which is the point where the three medians intersect, is also the center of mass.

- The centroid divides each median in a 2:1 ratio, with the longer segment being towards the vertex.

- For triangle PQR with side length PQ = 6 cm, the length of the median is given by the formula: median = (v3/2) * side.

- Thus, the length of the median from a vertex to the midpoint of the opposite side is: 6 * v3/2 = 3v3 cm.

- The centroid divides this median in a 2:1 ratio, thus the length from a vertex (e.g., P) to the centroid (L) is 2/3 of the total median length.

- Therefore, PL = (2/3) * 3v3 = 2v3 cm.

Answer: Option:3- 2v3 cm