Finding Swimming Pool Dimensions Given Its Perimeter
Apply the geometry problem-solving strategy to a real-world scenario where the perimeter of a rectangular shape and a relationship between its dimensions are given.
Problem: The perimeter of a rectangular swimming pool is 150 feet. The length is 15 feet more than the width. Find the length and width.
- Read: A rectangular pool has ft, and its length is 15 feet more than its width. Draw and label the figure.
- Identify: The length and width of the pool.
- Name: Let = the width. Because the length is "15 feet more than the width," the length is . Label the rectangle with width and length .
- Translate: Write the perimeter formula and substitute:
- Solve: Distribute to get . Combine like terms to get . Subtract 30 from both sides to get . Divide both sides by 4 to get . The width is 30 feet. Find the length: . The length is 45 feet.
- Check: , and .
- Answer: The length of the pool is 45 feet and the width is 30 feet.
This example applies the technique used in abstract rectangle problems—expressing both dimensions through a single variable via a stated relationship, then substituting into the perimeter formula—to a practical, real-world context. The algebraic structure (distribute, combine like terms, then isolate the variable in two steps) mirrors the simpler rectangle examples, reinforcing that the strategy works regardless of the size of the numbers or the setting of the problem.
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