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.