A width of the rectangle (the biggest line)
B height of the rectangle (the smallest line)
C width of the square

We know that 2 (A + B) = 18√2, so A + B = 9√2

We can also infer that A = 2B since A = 2 diagonal of the square and B = 1 diagonal of the square (see it on the figure to understand it more easily)

A = 3√2 and B = 6√2

From Pythagor, we have C² + C² = B²
<=> 2c² = (3√2)²
<=> 2c² = 9 * 2
<=> C = 3

So the perimeter of each square is 4 * 3 = 12

Perimeter of rectangle\(= 18\sqrt{2}\)

Lets say one side = x

other side \(= 9\sqrt{2} - x\)

When we divide the rectangle (as shown in fig), two squares would be formed

one side = x; other side \(= \frac{9\sqrt{2}}{2} - \frac{x}{2}\)

As square ABCD is formed, both sides should be equal

\(x = \frac{9\sqrt{2}}{2} - \frac{x}{2}\)

\(x = 3\sqrt{2}\)

Area of Square ABCD\(= 3\sqrt{2} * 3\sqrt{2} = 18\)

Area of inscribed square PQRS \(= \frac{1}{2} * 18 = 9\) (This is a thumb rule/property for inscribed square)

Length of a side of square PQRS \(= \sqrt{9} = 3\)

Perimeter of square PQRS= 3 * 4 = 12

Answer = B