A rectangular sheet of paper, when halved by folding it at the mid point of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?

[CAT 2004]

A

$$4 \sqrt{2}$$

B

$$2 \sqrt{2}$$

C

$$ \sqrt{2}$$

D

None of the above