Example

Finding the Length of a Rectangle Given Its Perimeter and Width

Apply the geometry problem-solving strategy using the rectangle perimeter formula when the perimeter and one dimension are known, requiring a two-step equation to find the missing dimension.

Problem: Find the length of a rectangle with perimeter 5050 inches and width 1010 inches.

  1. Read: A rectangle has P=50P = 50 in. and W=10W = 10 in.; find the length. Draw and label the figure.
  2. Identify: The length of the rectangle.
  3. Name: Let LL = the length.
  4. Translate: Write the perimeter formula and substitute the known values:

P=2L+2WP = 2L + 2W

50=2L+2(10)50 = 2L + 2(10)

  1. Solve: Multiply: 50=2L+2050 = 2L + 20. Subtract 2020 from both sides: 30=2L30 = 2L. Divide both sides by 22: 302=2L2\frac{30}{2} = \frac{2L}{2}, which gives 15=L15 = L.
  2. Check: Add all four sides: 15+10+15+10=5015 + 10 + 15 + 10 = 50, and 50=5050 = 50 \checkmark
  3. Answer: The length is 1515 inches.

Unlike computing the perimeter from two known sides — which involves only multiplication and addition — this problem requires solving a two-step linear equation: first subtracting the width-related term (2020) from the perimeter, then dividing by 22 to isolate the length. This demonstrates how the perimeter formula can be used in reverse to find a missing dimension when the perimeter and one side length are known.

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Updated 2026-04-21

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