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 answer is either 296,362,247,or 148
To solve this problem, we need to find the length of the diagonal of the square lot. Since the lot is square, all sides are equal in length.
To find the length of one side of the square lot, we can take the square root of the total area of 2 acres.
1 acre is 209 feet long, so 2 acres is 2 * 209 = 418 feet.
Therefore, one side of the square lot is √418 = 20.44 feet (rounded to two decimal places).
Now, to find the length of the diagonal, we can use the Pythagorean theorem.
The diagonal is the hypotenuse of a right triangle formed by two sides of the square lot. The sides of the square lot are equal in length, so the triangle is an isosceles right triangle.
The formula for the length of the hypotenuse of an isosceles right triangle is:
Diagonal = √(2 * side^2)
Plugging in the value of one side as 20.44 feet:
Diagonal = √(2 * 20.44^2) = √836.64016 = 28.92 feet (rounded to two decimal places).
Since Jamila wants to build a fence along the diagonal, she needs 28.92 feet (rounded to the nearest foot) of fencing.
The answer is 29 feet.