To determine how much fencing Jamila needs to build a diagonal fence in a square lot, we first need to confirm the dimensions of her 1-acre square lot.
An acre is defined as 43,560 square feet. Since the lot is square, we can find the length of each side by taking the square root of 43,560 square feet:
\[ \text{Side length} = \sqrt{43,560} \approx 208.71 \text{ feet} \]
For the sake of approximation, we use 209 feet as given.
Now, to find the length of the diagonal fence that runs from one corner of the square to the opposite corner, we can use the Pythagorean theorem. For a square, the diagonal \(d\) can be calculated as:
\[ d = \sqrt{(side\ length)^2 + (side\ length)^2} \]
Since both lengths are equal, this simplifies to:
\[ d = \sqrt{2 \times (side\ length)^2} = side\ length \times \sqrt{2} \]
Substituting the side length (209 feet):
\[ d = 209 \times \sqrt{2} \approx 209 \times 1.414 \approx 295.85 \text{ feet} \]
Rounding to the nearest foot, we find that the required length of fencing is approximately:
\[ \text{Length of fencing} \approx 296 \text{ feet} \]
Thus, Jamila needs 296 feet of fencing.
The correct answer is 296 feet.
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