Let $ w $ be the width of the original rectangular garden. The perimeter of the rectangle is $ 2(w+2w)=6w $, so the perimeter of the square is $ 12w $. The dimensions of the square are $ 3w\times 3w $ and its area is $ (3w)(3w)=9w^2 $, so set $ 9w^2=3600\text{ ft}^2 $ to find $ w^2=400 $ square feet. The area of the original rectangle is $ (2w)(w)=2w^2=2\cdot400\text{ ft}^2=\boxed{800} $ square feet.