Answer :
-- The smallest perimeter is about 24.98 feet ... that's 4 √39 .
-- There is no 'greatest'. If somebody gives you a gigantic perimeter
with an area of 39 square feet, I can always make a rectangle with the
same area and a bigger perimeter.
Example:
3-ft by 13-ft . . . Area = 39 ft² . . . Perimeter = 32 feet
1-ft by 39-ft . . . Area = 39 ft² . . . Perimeter = 80 feet
6-in by 78-ft . . . Area= 39 ft² . . . Perimeter = 157 feet
1-in by 468-ft . . Area = 39 ft² . . . Perimeter = 936-ft 2-in
0.1inch by 4,680-ft . . Area = 39 ft² . . . Perimeter = 9,360-ft 0.2-inch
(about 1.77 miles !)
