Let a rectangle \(ABCD\) of sides \(2\) and \(4\) be inscribed in another rectangle \(PQRS\) such that the vertices of the rectangle \(ABCD\) lie on the sides of the rectangle \(PQRS\). Let \(a\) and \(b\) be the sides of the rectangle \(PQRS\) when its area is maximum. Then \( (a+b)^2 \) is equal to:
