Example

Finding the Side Length of a Square Patio with Area 200 Square Feet

Apply the seven-step problem-solving strategy using the square area formula s=As = \sqrt{A} to find an unknown side length, producing a non-perfect-square result that must be rounded.

Problem: Mike and Lychelle want to make a square patio. They have enough concrete to pave an area of 200 square feet. Find the length of each side of the patio, rounded to the nearest tenth of a foot.

  1. Read: A square patio has A=200A = 200 square feet. Draw and label a square with sides ss.
  2. Identify: The length of a side of the square patio.
  3. Name: Let ss = the length of a side.
  4. Translate: Write the side-length formula and substitute the given area:

s=As = \sqrt{A}

s=200s = \sqrt{200}

  1. Solve: Evaluate: s=14.1421314.1s = 14.14213\ldots \approx 14.1.
  2. Check: 14.12=198.8114.1^2 = 198.81, which is close to 200. The small discrepancy is due to rounding the square root. A patio with side 14.1 feet is a reasonable size.
  3. Answer: Each side of the patio should be 14.1 feet.

Because 200 is not a perfect square, the exact side length is an irrational number that cannot be expressed as a terminating decimal. Rounding to the nearest tenth and then checking by squaring confirms the answer is close enough for a real-world application.

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Updated 2026-04-21

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