2.65 miles.
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You can't tell the shape or the distance around from the area. There are an infinite number of shapes and perimeters that all have areas of 100 acres. The shortest perimeter possible is a circle, with diameter (distance across) of 2,355 feet. The distance around it is 7,398 feet (about 1.4 miles). The shortest possible perimeter with straight sides is a square, 2,087 feet on every side. The distance around it is 8,348 feet (about 1.58 miles). If you stay with rectangles, there are an infinite number of different rectangles with different dimensions and different perimeters, that all have areas of 100 acres. The distance around every one of them is larger than 1.58 miles, and it can be anything up to infinity.
The area (acres) doesn't tell the perimeter. If the 2.5 acres is square, than the perimeter is 1,320 feet. If the 2.5 acres is a field that's 100-ft wide and 1,089-ft long, then the perimeter is 2,378 feet. The perimeter can be ANY distance longer than 1,320 feet.
One cannot determine how many miles a thousand acres is because miles and acres are completely different measurements. Acres measure area and miles measure distance. They cannot be compared.
1 square mile = 640 acres 2 square miles = 1,280 acres 3 square miles = 1,920 acres . . . 540 square miles = 345,600 acres