Problem:
A convex quadrilateral ABCD with area 2002 contains a point P in its interior such that PA=24,PB=32,PC=28, and PD=45. Find the perimeter of ABCD.
Answer Choices:
A. 42002
B. 28465
C. 2(48+2002)
D. 28633
E. 4(36+113) Solution:
it follows that the diagonals AC and BD are perpendicular and intersect at P. Thus, AB=242+322=40,BC=282+322=4113,CD=282+452=53, and DA=452+242=51. The perimeter of ABCD is therefore