the medians of $\triangle pqr$ are $\overline{pt}$, $\overline{qu}$, and $\overline{rs}$. they meet at a single point $v$. (in other words, $v$ is the centroid of $\triangle pqr$.) suppose $vu = 12$, $vs = 11$, and $pt = 27$. find the following lengths. note that the figure is not drawn to scale.

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Accepted Answer

# Explanation:
## Step1: Recall centroid properties
The centroid of a triangle divides each median into a ratio of $2:1$, with the longer segment being closer to the vertex. So, for median $PT$, $PV:VT = 2:1$, and $PT=PV + VT$. Given $PT = 27$, let $PV = 2x$ and $VT=x$. Then $2x + x=27$, so $3x = 27$, $x = 9$, and $PV=2\times9 = 18$.

## Step2: For median $QU$
Since $V$ is the centroid, $QV:VU=2:1$. Given $VU = 12$, then $QV=2\times VU=2\times12 = 24$.

## Step3: For median $RS$
Since $V$ is the centroid, $RV:VS = 2:1$. Given $VS = 11$, then $RV = 2\times11=22$. So $RS=RV + VS=22 + 11=33$.

# Answer:
$PV = 18$, $QV = 24$, $RS = 33$

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Question

Explanation:

Step1: Recall centroid properties

Step2: For median \(QU\)

Step3: For median \(RS\)

Answer: