In $△PQR$, $S$ and $T$ are points on side $PQ$ and $PR$ respectively. $ST$ is parallel to $QR$. If $S$ divides $PQ$ in the ratio $4:1$ and length of $QR$ is $15\text{cm}$, what is the length of $ST$?

Since $ST\parallel QR$, by Thales' theorem / Basic Proportionality Theorem, $△PST\sim △PQR$.Therefore, the ratios of their corresponding sides are equal:
$$\frac{ST}{QR}=\frac{PS}{PQ}$$
We are given that $S$ divides $PQ$ in the ratio $4:1$, meaning $PS:SQ=4:1$.Thus, the total length fraction for $PQ$ is:
$$PQ=PS+SQ=4+1=5\text{ parts}$$
So, $\frac{PS}{PQ}=\frac{4}{5}$.Substitute the values into the similarity ratio:
$$\frac{ST}{15}=\frac{4}{5}$$
$$ST=15\times \frac{4}{5}=3\times 4=12\text{cm}$$