-- 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