Question

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?

Answer 1

measure XT should be a half of TS

`\begin{gathered} XT=(74)/(2) \\ XT=37 \end{gathered}`

Measure TZ should be 2/3 of TW

`\begin{gathered} TZ=(2)/(3)(51) \\ TZ=34 \end{gathered}`

Measure ZW should be 1/3 of TW

`\begin{gathered} ZW=(1)/(3)(51) \\ ZW=17 \end{gathered}`

Measure XZ should be 1/3 of RX

use a relation between RZ and RX to find RX

`\begin{gathered} (2)/(3)\longrightarrow RZ \\ 1\longrightarrow RX \\ \\ (2)/(3)\longrightarrow42 \\ 1\longrightarrow RX \\ RX=42\cdot(3)/(2)=63 \\ RX=63 \end{gathered}`

Find XZ

`\begin{gathered} XZ=(63)/(3) \\ XZ=21 \end{gathered}`

measure SY should be obtained using a relation between ZY and SY

`\begin{gathered} (1)/(3)\longrightarrow ZY \\ 1\longrightarrow SY \\ \\ (1)/(3)\longrightarrow23 \\ 1\longrightarrow SY \\ SY=23\cdot(3)/(1)=69 \end{gathered}`

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