Answer:
[tex]RX=18\ cm[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
A centroid of a triangle is the point where the three medians of the triangle intersect. The centroid divides each median in a ratio of [tex]2:1[/tex]
In this problem the point X is the centroid of the triangle RST
so
[tex]\frac{RX}{XW} =\frac{2}{1}[/tex]
[tex]RX=2XW[/tex] ----> equation A
[tex]RW=RX+XW[/tex]
solve for RX
[tex]RX=RW-XW[/tex] -----> equation B
equate equation A and equation B
[tex]2XW=RW-XW[/tex]
[tex]3XW=RW[/tex]
[tex]XW=RW/3[/tex]
we have
[tex]RW=27\ cm[/tex]
substitute
[tex]XW=27/3=9\ cm[/tex]
Substitute in equation A
[tex]RX=2XW[/tex]
[tex]RX=2(9)=18\ cm[/tex]
