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First of all, an area of 100 feet is not possible since area is measured in square feet - not in feet. But suppose we overlook that fundamental error.

The area of a rectangle is not sufficient to determine its perimeter. It can have any value greater than 40 ft.

Let L be ANY length â‰¥ 10 ft and let W = 100/L ft.

Then, a rectangle with length L and width W has an area of L*W = L*100/L = 100 square feet. But since there are infinitely many choices for L, there are infinitely many perimeters (P).

For example,

L = 10 => W = 10 => P = 40

L = 100 => W = 1 => P = 202

L = 1000=> W = 0.1 => P = 2000.2

L = 10000=> W = 0.01 => P = 20000.02

You should see from that, there is no limit to how large L can be and so no limit on how large P can be.

Q: What is the perimeter of a rectangle with an area of 100 ft?

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2 ft

Width = Area/Length = 100/10 = 10 feet. Perimeter = 2*(L + W) = 2*(10 + 10)= 40 feet.

The area is not sufficient information to determine the perimeter. First of all, there is no reason to suppose that the area is rectangular as opposed to circular or triangular or some other simple or complicated shape. So, all that can be said is that the perimeter is greater than 178.97 feet, a perimeter that is attained when the area is a circle. If the area is a rectangle, it could be 25.49 ft * 100 ft so that the perimeter is approx 250.98 ft or 2.549 ft * 1000 ft and a perimeter of 2005.10 ft or 0.2549 ft * 10000 ft and a perimeter of 2000.51 ft or 0.0002549 ft * 10000000 ft and a perimeter of 2000000 ft. By making the rectangle thinner and longer, the perimeter can be increased without limit.

Area is 1.44 square feet Perimeter is 6 feet.

A 4 ft by 9 ft rectangle

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perimeter 182 ft. area 1960 square ft.

Half an acre = 21780 sq feet.This could have a perimeter of any length greater than (or equal to) 523.16 feet.If the area is in the form of a circle of radius 83.26 feet, it will have the minimum perimeter of 523.16 feet.Or, you can have a square of 147.6 ft giving a perimeter of 590.3 ft,or a rectangle of 150 ft * 145.2 ft - perimeter = 590.4 ftor a rectangle of 100 ft * 217.8 ft - perimeter = 635.6 ftor a rectangle of 10 ft * 2178 ft - perimeter = 4376 ftor a rectangle of 1 ft * 21780 ft - perimeter of = 43562 ftetc, with the perimeter increasing without limit.Or, the area could be circular giving the minim590 feet.

Width = Area/Length = 100/10 = 10 feet. Perimeter = 2*(L + W) = 2*(10 + 10)= 40 feet.

The area is not sufficient information to determine the perimeter. First of all, there is no reason to suppose that the area is rectangular as opposed to circular or triangular or some other simple or complicated shape. So, all that can be said is that the perimeter is greater than 178.97 feet, a perimeter that is attained when the area is a circle. If the area is a rectangle, it could be 25.49 ft * 100 ft so that the perimeter is approx 250.98 ft or 2.549 ft * 1000 ft and a perimeter of 2005.10 ft or 0.2549 ft * 10000 ft and a perimeter of 2000.51 ft or 0.0002549 ft * 10000000 ft and a perimeter of 2000000 ft. By making the rectangle thinner and longer, the perimeter can be increased without limit.

The area cannot be 15 feet since that is a measure of length, not area. In any case, information about the area cannot determine the perimeter; it can only put a lower limit on it. The perimeter can be anyhting from 15.49193 ft upwards. Consider the following rectangles, all with area = 15 square feet: a sqrt(15)*sqrt(15) rectangle will have a perimeter of 4*sqrt(15) = 15.49193 ft (approx). 1ft*15ft rectangle will have a perimeter of 32 feet 0.1ft*150ft rectangle: perimeter = 300.2 feet 0.01ft*1500ft rectangle: perimeter = 3000.02 ft 0.001ft*15000ft rectangle: perimeter = 30000.002 ft by now you should see that there is no upper limit to the perimeter.

Area is 1.44 square feet Perimeter is 6 feet.

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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A 4 ft by 9 ft rectangle

A rectangle measuring (200-ft x 240-ft) has Area = 48,000 square ft Perimeter = 880 ft

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