Consider all rectangles lying in the region

$$\left\{(x, y) \epsilon R \times R : 0 \leq x \leq \frac{\pi}{2} and 0 \leq y \leq 2\sin(2x)\right\}$$

and having one side on the $$x$$-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

A

$$\frac{3\pi}{2}$$

B

$$\pi$$

C

$$\frac{\pi}{2\sqrt{3}}$$

D

$$\frac{\pi\sqrt{3}}{2}$$