If Z is the centroid of delta RST, RZ=42, ST=74, TW=51, and ZY=23. find each measure. Are my measures correct? if not why?

measure XT should be a half of TS
[tex]\begin{gathered} XT=\frac{74}{2} \\ XT=37 \end{gathered}[/tex]Measure TZ should be 2/3 of TW
[tex]\begin{gathered} TZ=\frac{2}{3}(51) \\ TZ=34 \end{gathered}[/tex]Measure ZW should be 1/3 of TW
[tex]\begin{gathered} ZW=\frac{1}{3}(51) \\ ZW=17 \end{gathered}[/tex]Measure XZ should be 1/3 of RX
use a relation between RZ and RX to find RX
[tex]\begin{gathered} \frac{2}{3}\longrightarrow RZ \\ 1\longrightarrow RX \\ \\ \frac{2}{3}\longrightarrow42 \\ 1\longrightarrow RX \\ RX=42\cdot\frac{3}{2}=63 \\ RX=63 \end{gathered}[/tex]Find XZ
[tex]\begin{gathered} XZ=\frac{63}{3} \\ XZ=21 \end{gathered}[/tex]measure SY should be obtained using a relation between ZY and SY
[tex]\begin{gathered} \frac{1}{3}\longrightarrow ZY \\ 1\longrightarrow SY \\ \\ \frac{1}{3}\longrightarrow23 \\ 1\longrightarrow SY \\ SY=23\cdot\frac{3}{1}=69 \end{gathered}[/tex].