AMC 12 2002b Problem 24

A convex quadrilateral $ABCD$ with area $2002$ contains a point $P$ in its interior such that $PA = 24, PB = 32, PC = 28, PD = 45$. Find the perimeter of $ABCD$.

$\mathrm{(A)}\ 4\sqrt{2002} \mathrm{(B)}\ 2\sqrt{8465} \mathrm{(C)}\ 2(48+$ $\sqrt{2002}) \mathrm{(D)}\ 2\sqrt{8633} \mathrm{(E)}\ 4(36 + \sqrt{113})$