jamila keeps alpacas on a 2-acre, square lot near her home.
She has 6 alpacas and wants to build a fence diagonally to split the herd in two. if an acre is 209 feet long, how many feet, to the nearest foot, of fencing does jamila need?
The total area of Jamila's lot is 2 acres, which is equivalent to 2 * 209 = <<2*209=418>>418 feet.
Since the lot is square, the length of each side is the square root of the area, which is √418 ≈ 20.45 feet.
Jamila wants to divide the lot diagonally, which means she needs to build a fence from one corner of the lot to the opposite corner. This fence will divide the lot into two equal triangles.
To find the length of the diagonal, we can use the Pythagorean theorem, where the length of the diagonal is the hypotenuse and the two sides are the length of the side of the square lot.
Using the Pythagorean theorem: diagonal^2 = (side^2) + (side^2) = 2 * (side^2)
diagonal^2 = 2 * (20.45^2)
diagonal^2 ≈ 836.40
diagonal ≈ √836.40 ≈ 28.93 feet.
Since there are two equal diagonals, Jamila needs a total of 2 * 28.93 = 57.86 ≈ 58 feet of fencing to split the herd in two. Answer: \boxed{58}.