What is the greatest perimeter of a rectangle with the same area of 39 square feet?

There is no greatest perimeter.  The longer and skinnier you make the rectangle,
the greater its perimeter will become, while the area remains the same.

Example:

6-ft by 6.5-ft .. . . area = 39 sq ft, perimeter = 25 ft
3-ft by 13-ft . . . . area = 39 sq ft, perimeter = 32 ft
1-ft by 39-ft . . . . area = 39 sq ft, perimeter = 80 ft
0.1-ft by 390-ft . . area = 39 sq ft, perimeter = 780.2 ft.

No matter how great the perimeter of the rectangle is, it can always be made
greater, while keeping the same area.