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 ofthese 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
The two straight lines around the number indicate absolute value. Absolute value is the distance from the number to zero (essentially how many marks away on a number line).
