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It could be any amount greater than or equal to 1180.6 feet.

2 acres = 87120 sq feet. This has a minimum perimeter when it is in the shape of a square with sides 295.2 feet. This equals a perimeter of 4*295.2 = 1180.6 ft.

But the shape could be

290 x 300.4 requiring 1180.8 feet of Fencing, or

250 x 348.5 with perimeter of 1197.0 ft,

100 x 871.2 with perimeter of 1942.4 ft

10 x 8712 with perimeter of 17444 ft

1 x 87120 with a perimeter of 174242 ft.

The perimeter can be increased without limit by reducing one of the dimensions.

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Q: How many feet of fence is needed to fence in 2 acres?
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