There is no 'greatest' possible perimeter.
The smallest possible perimeter is obtained when the rectangle is
a square ... with sides that are √6 centimeters. Then, the perimeter
is 4√6 = about 9.8 .
But if the rectangle is not a square, then the longer and skinnier you
make it, the greater its perimeter becomes, and there is no limit.
You can make the perimeter as large as you want it to be, and still
keep the area at 6 square cm.
Examples: (All of these rectangles have area = 6 square centimeters.)
Dimensions of Approximate
the rectangle Perimeter
√6 x √6 9.798
2.5 x 2.4 9.8
2.7 x 2.222... 9.8444...
3 x 2 10
3.2 x 1.875 10.15
3.6 x 5/3 10.533...
4 x 1.5 11
4.5 x 4/3 11-2/3
4.8 x 1.25 12.1
5 x 1.2 12.4
6 x 1 14
9 x 2/3 19-1/3
12 x 0.5 25
15 x 0.4 30.8
18 x 1/3 36-2/3
24 x 0.25 48.5
30 x 0.2 60.4
36 x 1/6 72-1/3
42 x 1/7 84-2/7
48 x 1/6 96-1/3
60 x 0.1 120.2
120 x 0.05 240.1
600 x 0.01 1,200.02
6,000 x 0.001 12,000.002
