Question

In $△PQR$, points $S$ and $T$ are the mid-points of sides $PQ$ and $PR$ respectively.
If $ST=6.2$ then find the length of $QR$.

Answer 1

ST is parallel to QR (since ST is mid-point of PQ and PR) by proportionality theorem

$\begin{array}{c}\frac{PS}{PQ}=\frac{ST}{QR}\\ \Rightarrow \frac{PS}{PS+PS}=\frac{ST}{QR}\\ \Rightarrow \frac{1}{2}=\frac{ST}{QR}\\ \Rightarrow QR=2\times ST\\ \Rightarrow 2\times 6.2\\ \Rightarrow 12.4\end{array}$.