Four circles with centers A,B,C,and D are mutually tangent. The areas of circles A,B,C, and D are 25pi, 100pi, 16pi, and 225pi respectively. How many units are in the perimeter of quadrilateral ABCD?

If they can be arranged to be mutually tangent, the quadrilateral ABCD connects the centers of the circles, and has perimeter = 2(4 + 5 + 10 + 15) = 68