Jamila keeps alpacas on 1-acre, square lot near her home.

Question

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?

Answer 1

To determine how much fencing Jamila needs, we first need to find the length of the diagonal of the square lot.

Given that the lot is a square and each side of the square is 209 feet (since an acre is defined as 1 acre = 43,560 square feet, and in this case, it's implied that the square shape has each side measuring the square root of 43,560, which equates to approximately 209 feet per side), we can use the Pythagorean theorem to calculate the length of the diagonal.

The formula for the diagonal \(d\) of a square with side length \(s\) is:

\[ d = s \sqrt{2} \]

Substituting \(s = 209\) feet into the formula:

\[ d = 209 \sqrt{2} \]

Calculating \(\sqrt{2} \approx 1.414\):

\[ d \approx 209 \times 1.414 \approx 295.46 \]

Rounding to the nearest foot, Jamila will need approximately:

\[ \text{Fencing needed} \approx 295 \text{ feet} \]

Thus, Jamila needs about 295 feet of fencing.

Answer 2

are u sure

Answer 3

Let's double-check the calculation to ensure accuracy.

1. Determine the side length of the square lot: We are given that the lot is 1 acre, and each side of this square lot is 209 feet.

2. Calculate the diagonal of a square: The diagonal \(d\) of a square can be calculated using the formula: \[ d = s \sqrt{2} \] where \(s\) is the length of one side of the square.

3. Substituting the side length: \[ d = 209 \sqrt{2} \] Now, we know that \(\sqrt{2} \approx 1.414\).

4. Calculate the diagonal: \[ d \approx 209 \times 1.414 \approx 295.46 \]

5. Rounding to the nearest foot:

   • The diagonal calculated is approximately 295.46 feet.
   • When rounded to the nearest foot, this becomes 295 feet.

Thus, to split the herd in two, Jamila needs approximately 295 feet of fencing.

So yes, the original calculation is indeed correct: she will need about 295 feet of fencing.