Question:

$\Delta ABC \sim \Delta PQR \Rightarrow \dfrac{AB}{PQ} = \dfrac{BC}{QR} = \dfrac{AC}{PR} = \dfrac{\text{Perim}(ABC)}{\text{Perim}(PQR)}$. (1) [1.0 Mark]
Also $\Delta ABD \sim \Delta PQS$ (by SAS, as $AB/PQ = BD/QS$ and $\angle B = \angle Q$) $\Rightarrow \dfrac{AB}{PQ} = \dfrac{AD}{PS}$. (2) [1.0 Mark]
From (1) and (2): $\dfrac{\text{Perimeter}(\Delta ABC)}{\text{Perimeter}(\Delta PQR)} = \dfrac{AD}{PS}$. Proved! [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Proving perimeter ratio equals side ratio: 1.0 Mark
Proving $\Delta ABD \sim \Delta PQS \Rightarrow AB/PQ = AD/PS$: 1.0 Mark
Concluding proof: 1.0 Mark