we know that
In a triangle, a median is created by a vertex connected to the midpoint of the opposite side. Where all three lines intersect is the centroid, which is also the "center of mass"
In this problem
In the triangle TRS, the point Z is the centroid
[tex]RV=RZ+VZ[/tex]
The property of the centroid states that
[tex]RZ=\frac{2}{3} RV\\ \\ VZ=\frac{1}{3} RV[/tex]
Find the value of RV
we have
[tex]VZ=6\ inches[/tex]
so
[tex]RV=3VZ=3*6=18\ inches[/tex]
Find the value of RZ
[tex]RZ=\frac{2}{3} RV\\ \\RZ= \frac{2}{3}*18=12\ inches[/tex]
therefore
the answer is
RZ is [tex]12\ inches[/tex]
