How many miles around the perimeter of 120 acres rectangular in shape?

Answer 1

Very interesting question. The answer is: There is no answer, because knowing

the area doesn't tell you the shape or the perimeter.

There are an infinite number of rectangles that all have the same area but

different perimeters.

The shortest perimeter that can enclose 120 acres is a circle, with diameter of

about 2,580 ft, or 0.4886 mile. The perimeter (circumference) is 1.535 mile. (rounded)

The rectangle with the shortest perimeter that encloses 120 acres is a square

with sides of 2,286-ft. The perimeter is 9,145-ft or 1.732 miles.

The perimeter can be anything greater than that. The more long and skinny and

"unsquare" the rectangle is, the longer the perimeter is, for the same area.

Examples:

1,800-ft x 2,904-ft

Area = 120 acres

Perimeter = 9,408-ft = 1.782 miles

1,452-ft x 3,600-ft:

Area = 120 acres

Perimeter = 10,105-ft = 1.914 miles

726-ft x 7,200-ft:

Area = 120 acres

Perimeter = 15,862-ft = 3.002 miles

242-ft x 21,600-ft

Area = 120 acres

Perimeter = 43,684-ft = 8.273 miles

60.5-ft x 86,400-ft

Area = 120 acres

Perimeter = 172,921-ft = 32.750 miles