How many miles of perimeter fencing in 725 acres?

1 Answer

Answer :

It depends upon the shape of the area of 725 acres; the minimumlength is a circle with an area of 725 acres:1 acre = 1/640 square mile→ 725 acre = 725 ÷ 640 sq miles = 725/640 miles²Area circle = π × radius²→ radius = √(Area/π)Circumference = 2 × π × radius= 2 × π × √(Area/π)= √(4 × π × Area)= √(4 × π × 725/640 miles²)= √(145π/32) miles≈ 3.773 milesYou will require at least approx 3.773 miles of Fencing toenclose an area of 725 acres.ie the fencing will be greater than or equal to approx 3.773miles - there is no upper limit to the amount of fencing you willneed.--------------------------------------------------------------------An acre was define as the amount of and an ox could plough in aday and is the area of a furrow long(a furlong = 1/8 mile) by a chain (= 1/80 mile).If you scale this rectangle up to 725 acres, it will be √725larger in each direction, ie it will be a rectangle (√725)/8 milesby (√725)/80 miles→perimeter = 2 × ((√725)/8 + (√725)/80) miles= (2 × √725)(10 + 1)/80 miles= (11√725)/40 miles≈ 7.405 milesIf you had 725 of the furlong by chain fields next to each otheralong the furlong side, it would form a rectangle 1 furlong by 725chains which gives:perimeter = 2 × (1/8 + 725 × 1/80) miles= 726/40 miles= 18 3/20 miles= 18.15 miles.If the 725 files were next to each other along the chain side,it for form a rectangle 1 chain by 725 furlongs which gives:perimeter = 2 × (1/80 + 725 × 1/80) miles= 7251/40 miles= 181 11/40 miles= 181.275 miles

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