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

1 answer

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.

Similar Questions
    1. answers icon 1 answer
    1. answers icon 3 answers
  1. Here is the graphGallons of pain X 1 to 6 Area (square feet) Y 200 to 1200 Point A (2, 800) Point B (3, 1200) The slope of the
    1. answers icon 1 answer
  2. still working on this and need additional helptwo houses are for sale on the same street. the second house has 1000 square feet
    1. answers icon 1 answer
more similar questions