To determine which of the garden areas has a rational number for the side length, we need to find the square root of each area. The side length \( s \) of a square garden can be calculated using the formula:
\[ s = \sqrt{\text{Area}} \]
Now let's calculate the side lengths for the given areas:
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Area: 144 m² \[ s = \sqrt{144} = 12 \text{ m} \quad (\text{Rational}) \]
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Area: 32 m² \[ s = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \text{ m} \quad (\text{Irrational}) \]
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Area: 72 m² \[ s = \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \text{ m} \quad (\text{Irrational}) \]
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Area: 250 m² \[ s = \sqrt{250} = \sqrt{25 \times 10} = 5\sqrt{10} \text{ m} \quad (\text{Irrational}) \]
Out of the four areas, only the area of 144 m² results in a rational side length of 12 meters. The other areas result in irrational side lengths. Thus, the area with a rational number of meters as the side length is:
\[ \text{Area: 144 m²} \]
3 answers