4 square houses have the following areas in feet: 810, 1200, 900, 1040. Whivh area has a rational number of meters as the side length?

Answer 1

To find out which of the given areas corresponds to a rational number for the side length of a square house, we need to take the square root of each area and check if it results in a rational number.

The area of a square is given by the formula \( A = s^2 \), where \( s \) is the side length. Thus, to find the side length, we can take the square root of each area.

Now, let's calculate the side lengths for each area:

1. For the area of 810 square feet: \[ s = \sqrt{810} \approx 28.46 \text{ feet (irrational)} \]

2. For the area of 1200 square feet: \[ s = \sqrt{1200} = \sqrt{100 \times 12} = 10\sqrt{12} \approx 34.64 \text{ feet (irrational)} \]

3. For the area of 900 square feet: \[ s = \sqrt{900} = 30 \text{ feet (rational)} \]

4. For the area of 1040 square feet: \[ s = \sqrt{1040} = \sqrt{16 \times 65} = 4\sqrt{65} \approx 32.25 \text{ feet (irrational)} \]

Among the areas given, the area of 900 square feet has a side length of 30 feet, which is a rational number.

Now, to convert square feet to square meters, we can use the conversion factor: 1 square foot = 0.092903 square meters.

To express the side length in meters, we can convert feet to meters: \[ 30 \text{ feet} \times 0.3048 \text{ meters/foot} = 9.144 \text{ meters} \]

Thus, the only area that results in a rational number of meters for the side length is for the area of 900 square feet.

Answer 2

Are you sure dude?

Answer 3

Let's double-check the calculations more carefully to ensure accuracy.

For each area, we will find the side length and check if it is a rational number.

1. Area = 810 square feet: \[ s = \sqrt{810} = \sqrt{90 \times 9} = 9\sqrt{90} \approx 28.46 \text{ feet (irrational)} \]

2. Area = 1200 square feet: \[ s = \sqrt{1200} = \sqrt{100 \times 12} = 10\sqrt{12} \approx 34.64 \text{ feet (irrational)} \]

3. Area = 900 square feet: \[ s = \sqrt{900} = 30 \text{ feet (rational)} \]

4. Area = 1040 square feet: \[ s = \sqrt{1040} = \sqrt{16 \times 65} = 4\sqrt{65} \approx 32.25 \text{ feet (irrational)} \]

So, the conclusions are:

• Area 810: Irrational side length
• Area 1200: Irrational side length
• Area 900: Rational side length (30 feet)
• Area 1040: Irrational side length

The only area that provides a rational number for the side length is indeed 900 square feet. Therefore, my original conclusion is correct. The side length is 30 feet, which converts to approximately 9.144 meters.

If you have a specific concern or a different interpretation, please let me know!