2006 AMC 12B Problem 21

Rectangle ABCD has area 2006. An ellipse with area 2006\pi passes through A and C and has foci at B and D. What is the perimeter of the rectangle? (The area of an ellipse is ab\pi where 2a and 2b are the lengths of the axes.)

\mathrm{(A)}\ \frac {16\sqrt {2006}}{\pi} \qquad \mathrm{(B)}\ \frac {1003}4 \qquad \mathrm{(C)}\ 8\sqrt {1003} \qquad \mathrm{(D)}\ 6\sqrt {2006} \qquad \mathrm{(E)}\ \frac {32\sqrt {1003}}\pi

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.