Jamila keeps alpacas on a 1-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 diagonal of a square can be calculated using the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the square lot are equal to the square root of 1 acre, which is the square root of 209 feet, since 1 acre is 209 feet long.
Using the Pythagorean theorem, the diagonal of the square lot can be found as follows:
Diagonal = √(side^2 + side^2)
= √(209^2 + 209^2)
= √(43,681 + 43,681)
= √87,362
≈ 295.5 feet
Therefore, Jamila needs approximately 295.5 feet of fencing to split her herd of alpacas.