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