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The length of a rectangular swimming pool is twice as long as its width. If the perimeter of the pool is 120 feet, then what is the width of the pool, in feet?

The length of a rectangular swimming pool is twice as long as its width. If the perimeter of the pool is 120120 feet, then what is the width of the pool, in feet?

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Math Problemsright chevron icon
Algebra 2right chevron icon
Pythagorean Theorem and its converseright chevron icon

Full solution

Q. The length of a rectangular swimming pool is twice as long as its width. If the perimeter of the pool is 120120 feet, then what is the width of the pool, in feet?
  1. Define Variables: Let's denote the width of the pool as ww and the length as ll. According to the problem, the length is twice the width, so we can write l=2wl = 2w.
  2. Perimeter Equation: The perimeter PP of a rectangle is given by P=2l+2wP = 2l + 2w. \newlineWe know that the perimeter is 120120 feet, so we can set up the equation 120=2l+2w120 = 2l + 2w.
  3. Substitute Length: Substitute ll with 2w2w in the perimeter equation to get 120=2(2w)+2w120 = 2(2w) + 2w.
  4. Simplify Equation: Simplify the equation: \newline120=4w+2w120 = 4w + 2w
  5. Combine Like Terms: Combine like terms: \newline120=6w120 = 6w
  6. Solve for Width: Divide both sides by 66 to solve for ww: \newlinew=1206w = \frac{120}{6}
  7. Calculate Width: Calculate the width: \newlinew=20w = 20 feet

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