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)
Responses

1040
1040

810
810

1200
1200

900

Answer 1

To determine which area has a rational number of meters as the side length, we need to convert each area from square feet to square meters using the conversion factor \(1 \text{ square foot} = 0.092903 \text{ square meters}\).

First, calculate the side length in feet for each area:

1. \( A = s^2 \) where \( A \) is the area and \( s \) is the side length.
2. \( s = \sqrt{A} \) is the formula to find the side length.

Now, we calculate the side lengths for each area:

1. For \( 810 \, \text{ft}^2 \):
\[
s = \sqrt{810} = 9 \sqrt{90} \text{ (irrational)}
\]

2. For \( 1200 \, \text{ft}^2 \):
\[
s = \sqrt{1200} = 10 \sqrt{12} \text{ (irrational)}
\]

3. For \( 900 \, \text{ft}^2 \):
\[
s = \sqrt{900} = 30 \text{ (rational)}
\]

4. For \( 1040 \, \text{ft}^2 \):
\[
s = \sqrt{1040} = 4 \sqrt{65} \text{ (irrational)}
\]

Next, since we want which area actually has a rational number of meters as the side length, let's convert the side length of the area 900 to meters.

Converting the side length in feet to meters:
\[
s_{900} = 30 \text{ ft} = 30 \times 0.3048 \approx 9.144 \text{ m} \text{ (which is rational)}
\]

The side lengths for the other areas are irrational, but the area that has a rational number as the side length is:

**900**.