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The rectangle with the smallest perimeter for a given area is the square. The rectangle with the greatestperimeter for a given area can't be specified. The longer and skinnier you make the rectangle, the greater its perimeter will become. No matter how great a perimeter you use to enclose 24 ft2, I can always specify a longer perimeter. Let me point you in that direction with a few examples: 6 ft x 4 ft = 24 ft2, perimeter = 20 ft 8 ft x 3 ft = 24 ft2, perimeter = 22 ft 12 ft x 2 ft = 24 ft2, perimeter = 28 ft 24 ft x 1 ft = 24 ft2, perimeter = 50 ft 48 ft x 6 inches = 24 ft2, perimeter = 97 ft 96 ft x 3 inches = 24 ft2, perimeter = 192.5 ft 288 ft x 1 inch = 24 ft2, perimeter = 576ft 2inches No matter how great a perimeter you find to enclose 24 ft2, I can always specify a rectangle with the same area and a longer perimeter.

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Q: A rectangle had an area of 24ft2 what is the length and width of the rectangle with the greatest perimeter?
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