$R$ is the midpoint of line seqment $\overline{PT}$, and $Q$ is the midpoint of line segment $\overline{PR}$. If $S$ is a point between $R$ and $T$ such that the length of segment $\overline{QS}$ is $13$ and the length of segment $\overline{PS}$ is $21$, what is the length of segment $\overline{ST}$?

เฉลยละเอียด

[STEP]Draw the diagram and mark the given points and distances[/STEP]

Since $\overline{PS}=21$ and $\overline{QS}=13$,
the different part $\overline{PQ}=21-13=8$.

[STEP]Calculate $\overline{QR}$ and $\overline{RS}$[/STEP]

Therefore $\overline{QR}=\overline{PQ}=8$ and $\overline{RS}=\overline{QS}-\overline{QR}=13-8=5$.

[STEP]Calculate $\overline{ST}$[/STEP]

From $\overline{RT}=\overline{PR}=\overline{PQ}+\overline{QR}=8+8=16$, we have $\overline{ST}=\overline{RT}-\overline{RS}=16-5=11$

[ANS]$\overline{ST}=11$[/ANS]

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