Question 1059261
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In {{{highlight(triangle)}}} MNK, MS and NR are medians. If MS = 15, NR = 18, and MN = 21, what is the perimeter of {{{highlight(triangle)}}} PRS 
(P is the point of concurrency) and why?
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<pre>
In triangle PRS the side RS is the mid-segment of the triangle MNK.

The length |RS| is half of the length MN: |RS| = {{{1/2}}}*|MN| = {{{(1/2)*21}}} = 10.5 units.


The side PR of the triangle PRS has the length of (1/3) of the length of the median NR: |PR| = {{{1/3}}}*|NR| = {{{(1/3)*18}}} = 6 units.


The side PS of the triangle PRS has the length of (1/3) of the length of the median MS: |PS| = {{{1/3}}}*|MS|}}} = {{{(1/3)*15}}} = 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  <A HREF=https://www.algebra.com/algebra/homework/Triangles/Medians-of-a-triangle-are-concurrent.lesson>Medians of a triangle are concurrent</A>  in this site.


<U>Answer</U>.  The perimeter of the triangle PRS is  21.5  units.
</pre>

Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lesson is the part of this online textbook under the topic "<U>Properties of triangles</U>".