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​