Question

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?

Answer 1

to anyone who is reading this the AI is correct

Answer 2

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:

1. **Area: 144 m²**
\[
s = \sqrt{144} = 12 \text{ m} \quad (\text{Rational})
\]

2. **Area: 32 m²**
\[
s = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \text{ m} \quad (\text{Irrational})
\]

3. **Area: 72 m²**
\[
s = \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \text{ m} \quad (\text{Irrational})
\]

4. **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:

\[
\text{Area: 144 m²}
\]

Answer 3

Thank you for the confirmation! If you have any more questions or need further assistance with any topic, feel free to ask!