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

There is no greatest perimeter. The longer and skinnier you make the rectangle,

the greater its perimeter becomes, even though its area remains the same.

Look at this:

√39 by √39, Area = 39, Perimeter = 4 √39 = about 24.98

6 by 6.5, Area = 39, Perimeter = 25

3 by 13, Area = 39, Perimeter = 32

2 by 19.5, Area = 39, Perimeter = 43

1 by 39, Area = 39, Perimeter = 80

0.1 by 390, Area = 39, Perimeter = 780.2

0.00001 by 3,900,000, Area = 39, Perimeter = 7,800,000.2