Consider all rectangles lying in the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{R} \times \mathbb{R}: 0 \leq \…

Consider all rectangles lying in the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{R} \times \mathbb{R}: 0 \leq \mathrm{x} \leq \frac{\pi}{2} \text { and } 0 \leq \mathrm{y} \leq 2 \sin (2 \mathrm{x})\right\} \) and having one side on the \(\mathrm{x}\)-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

[JEE Advanced 2020]