Refer diagram below:

Attachment:

set21-q8_Q.GIF [ 3.47 KiB | Viewed 695 times ]
Perimeter of rectangle \(= \frac{18}{\sqrt{2}}\)

Lets say one side = x

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

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

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

As square ABCD is formed, both sides should be equal

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

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

Area of Square ABCD\(= \frac{3}{\sqrt{2}} * \frac{3}{\sqrt{2}} = \frac{9}{2}\)

Area of inscribed square PQRS \(= \frac{1}{2} * \frac{9}{2} = \frac{9}{4}\)

Length of a side of square PQRS \(= \sqrt{\frac{9}{4}} = \frac{3}{2}\)

Perimeter of square PQRS\(= \frac{3}{2} * 4 = 6\)

Bunuel, can you kindly update OA?

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