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A rectangular sheet of paper, when halved by folding it at mid-point of its longer side, results in a rectangle, whose longer and shorter sides are in 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?

  1. $4 \sqrt{2}$
  2. $2 \sqrt{2}$
  3. $ \sqrt{2}$
  4. None of the above
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