Question

Four square houses have the following areas in feet: 810, 1200, 900, 1040. Which area has a rational number of meters as the side length?(1 point)
810
1040
900
1200

Answer 1

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:

1. For 810 ft²:
\[
\text{Side length} = \sqrt{810} \approx 28.46 \text{ ft}
\]

2. For 1200 ft²:
\[
\text{Side length} = \sqrt{1200} \approx 34.64 \text{ ft}
\]

3. For 900 ft²:
\[
\text{Side length} = \sqrt{900} = 30 \text{ ft}
\]

4. 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:

1. **Area 810**:
\[
\text{Side length in meters} = 28.46 \times 0.3048 \approx 8.68 \text{ m}
\]

2. **Area 1200**:
\[
\text{Side length in meters} = 34.64 \times 0.3048 \approx 10.56 \text{ m}
\]

3. **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)

4. **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**.