SOLUTION: In MNK, MS and NR are medians. If MS = 15, NR = 18, and MN = 21, what is the perimeter of PRS (P is the point of concurrency) and why?

In triangle PRS the side RS is the mid-segment of the triangle MNK.

The length |RS| is half of the length MN: |RS| = *|MN| =  = 10.5 units.


The side PR of the triangle PRS has the length of (1/3) of the length of the median NR: |PR| = *|NR| =  = 6 units.


The side PS of the triangle PRS has the length of (1/3) of the length of the median MS: |PS| = *|MS|}}} =  = 5 units.


Now, the perimeter of the triangle PRS is |RS| + |PR| + |PS| = 10.5 + 6 + 5 = 21.5 units.


We used the fact that in any triangle the concurrency point of medians divides each median in the ratio 2:1 counting from the vertex to the base.


See the lesson  Medians of a triangle are concurrent  in this site.


Answer.  The perimeter of the triangle PRS is  21.5  units.