In triangle $PQR$, a line through point $S$ on side $PQ$ is drawn parallel to $QR$ intersecting $PR$ at $T$. If $PS=4\text{ cm}$, $SQ=6\text{ cm}$ and $QR=15\text{ cm}$, find the length of $ST$ (in cm).

Step-by-step solution

1. Since $ST\parallel QR$, triangles $△PST$ and $△PQR$ are similar (AA similarity).
2. Corresponding sides are in the same ratio: $\frac{PS}{PQ}=\frac{ST}{QR}$.
3. Compute $PQ=PS+SQ=4\text{ cm}+6\text{ cm}=10\text{ cm}.$
4. Find the ratio $\frac{PS}{PQ}=\frac{4}{10}=\frac{2}{5}.$
5. Use the ratio to find $ST$: $ST=\frac{2}{5}\times QR=\frac{2}{5}\times 15\text{ cm}=6\text{ cm}.$

Concept tested: Similarity of triangles with parallel line

Published 21 August 2026 · How this solution was prepared and checked

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