Four square gardens have the following areas in square meters: 144, 32, 72, and 250. Which area has a rational number of meters as the side length? (1 point)
The area that has a rational number of meters as the side length must have a perfect square area.
144 is a perfect square since it is 12 * 12 = (12)^2.
32 is not a perfect square.
72 is not a perfect square.
250 is not a perfect square.
Therefore, the area of 144 square meters has a rational number of meters as the side length.
what is the answer in numbers
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To determine which area has a rational number as the side length, we need to find the area that has a perfect square as its value. A perfect square is a number that can be expressed as the square of an integer.
Let's calculate the square roots of the given areas:
- Square root of 144: √144 = 12 (a rational number)
- Square root of 32: √32 ≈ 5.66 (an irrational number)
- Square root of 72: √72 ≈ 8.49 (an irrational number)
- Square root of 250: √250 ≈ 15.81 (an irrational number)
From the calculations above, we can see that the only area with a rational number as its square root (side length) is 144. Therefore, the area with a rational number of meters as the side length is 144 square meters.
To determine which area has a rational number of meters as the side length, we need to identify an area that has a perfect square as its value.
Step 1: Find the square root of each area.
The square root of 144 is 12.
The square root of 32 is approximately 5.66.
The square root of 72 is approximately 8.49.
The square root of 250 is approximately 15.81.
Step 2: Identify which square root is a whole number (integer).
Since the square root of 144 is 12, this means that the side length is a whole number and, therefore, a rational number. Thus, the area of 144 square meters has a rational number as the side length.
Conclusion: The area of 144 square meters has a rational number as the side length.