To find the length of fencing that Jamila needs to split her square lot diagonally, we first need to determine the diagonal length of the lot.
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Calculate the diagonal of the square lot: The formula for the diagonal \( d \) of a square with side length \( s \) is given by: \[ d = s \sqrt{2} \]
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Determine the side length of the lot: Since 1 acre is equivalent to a square with each side being \( \sqrt{1 , \text{acre}} \), and given that 1 acre is \( 43,560 , \text{square feet} \), first calculate the side length: \[ s = \sqrt{43,560} \approx 209 , \text{feet} \]
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Calculate the diagonal using the side length: Now we can plug in the side length into the diagonal formula: \[ d = 209 , \text{feet} \times \sqrt{2} \]
Since \( \sqrt{2} \) is approximately \( 1.414 \): \[ d \approx 209 \times 1.414 \approx 295.652 , \text{feet} \]
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Round the diagonal length to the nearest foot: Approximately, \( 295.652 \) feet rounds to \( 296 \) feet.
Therefore, the length of fencing that Jamila needs is 296 feet.