Let AD be the perpendicular dropped from A to the side BC and PS be the perpendicular dropped from P to the side QR respectively.
Since, ΔABC∼ΔPQR, we have ΔABD∼ΔPQS.
Therefore,
AB/PQ=AD/PS=BC/QR ⇒arΔABC/arΔPQR=AD×BC/PS×QR =AB/PQ×AB/PQ =AB^2/PQ^2 =1/9
Let AD be the perpendicular dropped from A to the side BC and PS be the perpendicular dropped from P to the side QR respectively.
Since, ΔABC∼ΔPQR, we have ΔABD∼ΔPQS.
Therefore,
AB/PQ=AD/PS=BC/QR
⇒arΔABC/arΔPQR=AD×BC/PS×QR
=AB/PQ×AB/PQ
=AB^2/PQ^2
=1/9