There is no "greatest" possible perimeter.
There's a smallest possible perimeter. That's a square.
Since the area is 6 square centimeters, each side of the square is
√6 = about 2.45 cm, and the perimeter is about 9.8 cm (rounded).
But there's no 'greatest' perimeter. You can take that square
and if you're careful, you can make it into rectangles that all have
the same area ... 6 square cm ... but the longer and skinnier
you make it, the greater the perimeter will be.
You can give me a number as big as you want, and I can make
a rectangle with a perimeter of your number, but an area of only
6 square centimeters !
Here are some few examples. They all have
the same area, but different perimeters:
2.45 cm by 2.45 cm ... Area = 6 square cm ... Perimeter = 9.8 cm
2 cm by 3 cm ... Area = 6 square cm ... Perimeter = 10 cm
1.5 cm by 4 cm ... Area = 6 square cm ... Perimeter = 11 cm
1.2 cm by 5 cm ... Area = 6 square cm ... Perimeter = 12.4 cm
1 cm by 6 cm ... Area = 6 square cm ... Perimeter = 14 cm
0.8 cm by 7.5 cm ... Area = 6 square cm ... Perimeter = 16.6 cm
0.6 cm by 10 cm ... Area = 6 square cm ... Perimeter = 21.2 cm
0.5 cm by 12 cm ... Area = 6 square cm ... Perimeter = 25 cm
0.4 cm by 15 cm ... Area = 6 square cm ... Perimeter = 30.8 cm
0.3 cm by 20 cm ... Area = 6 square cm ... Perimeter = 40.6 cm
0.2 cm by 30 cm ... Area = 6 square cm ... Perimeter = 60.4 cm
0.1 cm by 60 cm ... Area = 6 square cm ... Perimeter = 120.2 cm
0.001cm by 6,000cm ... Area = 6 square cm ... Perimeter = 12,000.2 cm