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Geometry Level 3

Two congruent squares ABCDABCD and PQRSPQRS are positioned such that they share a common area defined by ΔPQB\Delta PQB. The ratio of the area of ΔPQB\Delta PQB to the area of polygon AQRSPCDAQRSPCD is 322 \dfrac{3}{22} .

If the side length of both squares is ss, then the perimeter of polygon AQRSPCDAQRSPCD is mns\dfrac{m}{n}s, where mm and nn are coprime positive integers. Find m+nm+n.

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