To find which areas have a rational number of meters as the side length, we need to find the square root of each area and check if it is a rational number. A number is rational if it can be expressed as the quotient of two integers.
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For an area of 144 m²: \[ \sqrt{144} = 12 \quad (\text{rational}) \]
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For an area of 32 m²: \[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \quad (\text{irrational}) \]
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For an area of 72 m²: \[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \quad (\text{irrational}) \]
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For an area of 250 m²: \[ \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \cdot \sqrt{10} = 5\sqrt{10} \quad (\text{irrational}) \]
The only area that has a rational number as the side length is 144 m², which has a side length of 12 meters.