Tomas drew a rectangle with an area of 6 square centimeters. what is the greatest possible perimeter for this rectangle?

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

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