How many feet of fence around 100 acres?

Answer 1

Anywhere from approx 17398.6 ft upwards.

The minimum length of fence to enclose 100 acres is when the area is a circle. In which case the length of fence required = circumference of the circle:

1 acre = 43560 sq ft

area = π × radius²

→ radius = √(area ÷ π)

length = 2 × π × radius = 2 × π × √(area ÷ π) = 2 × √(area × π) = 2 × √(100 × 43560 sq ft × π) ≈ 7398.5 ft

Any other shape with an area of 100 acres will have a longer perimeter; if the shape is a fractal (like the coastline of a country) then the perimeter is infinite.