Question

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

Answer 1

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.