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Wyoming is approximately a square-shaped state. If the area of Wyoming is about 97,818 square miles, you can find the length of each side.(4 points)

Put responses in the correct input to answer the question.

A. Find the length of one dimension of Wyoming by (Response area) . The length of one side is approximately (Response area)

B. Find the perimeter of Wyoming by (Response area) . The Perimeter of Wyoming is approximately (Response area)

Please explain.

1 answer

To find the length of one side of Wyoming and the perimeter, we can use the following calculations:

A. Finding the length of one side

  1. Area: The area \(A\) of a square is calculated using the formula: \[ A = s^2 \] where \(s\) is the length of one side.

  2. Given the area of Wyoming is approximately 97,818 square miles, we can set up the equation: \[ s^2 = 97,818 \]

  3. To find \(s\), we take the square root of both sides: \[ s = \sqrt{97,818} \approx 313 \] (This value is rounded to the nearest whole number.)

Thus, one side of Wyoming is approximately 313 miles.

B. Finding the perimeter

  1. Perimeter: The perimeter \(P\) of a square is calculated using the formula: \[ P = 4s \]

  2. Using the side length we found: \[ P = 4 \times 313 \approx 1,252 \] (Again, this value is rounded to the nearest whole number.)

Thus, the perimeter of Wyoming is approximately 1,252 miles.

Summary

  • The length of one side of Wyoming is approximately 313 miles.
  • The perimeter of Wyoming is approximately 1,252 miles.