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# How do you find the area of a rectangle with only the perimeter?

Wiki User

2009-03-17 03:04:28

The clever person might realize that, though an infinite number of rectangles can be created with a fixed perimeter, there is a maximum and minimum area that any rectangle formed under the constriction can have. And we can work with that. The minimum area will be "near" zero. (With an area "at" zero, the rectangle will collapse and/or disappear.) The rectangle with "maximumized" area for a fixed perimeter will be a square. Its side (designated by "s") will be one fourth of the perimeter (designated by "p"). If s = p/4 and we use the formula for finding the area (As) of a square substituing our "p/4" for the side length "s" we will get the equation: As = (p/4)2 Our rectangle(s) will all have an area (Ar) within this range: Zero is less than Ar which is less than or equal to (p/4)2 Though we couldn't come up with a precise answer, we came up with the next best thing with the information supplied.

Wiki User

2009-03-17 03:04:28
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