To determine which area has a rational number of meters as the side length, we need to find the square root of each area and convert it from feet to meters.
The side length of a square is found by taking the square root of the area. The conversion from feet to meters is given by the factor \(1 \text{ ft} = 0.3048 \text{ m}\).
Now, let's calculate the side lengths:
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For 810 ft²: \[ \text{Side length} = \sqrt{810} \approx 28.46 \text{ ft} \]
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For 1200 ft²: \[ \text{Side length} = \sqrt{1200} \approx 34.64 \text{ ft} \]
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For 900 ft²: \[ \text{Side length} = \sqrt{900} = 30 \text{ ft} \]
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For 1040 ft²: \[ \text{Side length} = \sqrt{1040} \approx 32.25 \text{ ft} \]
Now, we will check which of these side lengths, when converted to meters, results in a rational number:
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Area 810: \[ \text{Side length in meters} = 28.46 \times 0.3048 \approx 8.68 \text{ m} \]
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Area 1200: \[ \text{Side length in meters} = 34.64 \times 0.3048 \approx 10.56 \text{ m} \]
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Area 900: \[ \text{Side length in meters} = 30 \times 0.3048 = 9.144 \text{ m} \] (which is rational since \(9.144\) is a terminating decimal)
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Area 1040: \[ \text{Side length in meters} = 32.25 \times 0.3048 \approx 9.83 \text{ m} \]
Among these calculations, the only area that results in a rational number when calculated in meters is the area of 900 ft².
Thus, the answer is: 900.
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