Example

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 150150 feet. The length is 1515 feet more than the width. Find the length and width.

  1. Read: A rectangular pool has P=150P = 150 ft, and its length is 1515 feet more than its width. Draw and label the figure.
  2. Identify: The length and width of the pool.
  3. Name: Let ww = the width. Because the length is "1515 feet more than the width," the length is w+15w + 15. Label the rectangle with width ww and length w+15w + 15.
  4. Translate: Write the perimeter formula and substitute:

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

150=2(w+15)+2w150 = 2(w + 15) + 2w

  1. Solve: Distribute: 150=2w+30+2w150 = 2w + 30 + 2w. Combine like terms: 150=4w+30150 = 4w + 30. Subtract 3030 from both sides: 120=4w120 = 4w. Divide both sides by 44: 30=w30 = w. The width is 3030 feet. Find the length: 30+15=4530 + 15 = 45. The length is 4545 feet.
  2. Check: P=2(45)+2(30)=90+60=150P = 2(45) + 2(30) = 90 + 60 = 150, and 150=150150 = 150 \checkmark
  3. Answer: The length of the pool is 4545 feet and the width is 3030 feet.

This example applies the same 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.

0

1

Updated 2026-04-21

Contributors are:

Who are from:

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.3 Math Models - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Related
Learn After