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Geometry Level 4

Two congruent squares \(ABCD\) and \(PQRS\) are positioned such that they share a common area defined by \(\Delta PQB\). The ratio of the area of \(\Delta PQB\) to the area of polygon \(AQRSPCD\) is \( \dfrac{3}{22} \).

If the side length of both squares is \(s\), then the perimeter of polygon \(AQRSPCD\) is \(\dfrac{m}{n}s\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).

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