Solving for the Dimensions of a Rectangular Swimming Pool

Understanding the dimensions of a swimming pool can be crucial for various reasons, such as planning the layout of your backyard, calculating the amount of water needed, and even deciding on the appropriate filtration system. In this article, we will explore a classic algebraic problem using a rectangular swimming pool as an example. Let's dive into the mathematical challenge step-by-step.

Problem Statement

The length of a rectangular swimming pool is 12 feet more than twice its width. The perimeter of the pool is 120 feet. What are the dimensions of the pool?

Solving the Problem

Let's begin by defining the variables and setting up the equations based on the given information.

Step 1: Define the Variables

Let ( L ) represent the length of the pool, and ( W ) represent the width. According to the problem, we know the following:

The length is 12 feet more than twice the width: ( L 12 2W ). The perimeter of the pool is 120 feet.

Step 2: Set Up the Perimeter Equation

The formula for the perimeter ( P ) of a rectangle is given by:

[ P 2L 2W ]

Substituting the given perimeter, we get:

[ 120 2L 2W ]

Step 3: Substitute the Length Expression

Since ( L 12 2W ), we can substitute this expression into the perimeter equation:

[ 120 2(12 2W) 2W ]

Step 4: Simplify the Equation

First, distribute the 2 in the equation:

[ 120 24 4W 2W ]

Combine like terms:

[ 120 24 6W ]

Step 5: Isolate the Variable

To solve for ( W ), subtract 24 from both sides of the equation:

[ 120 - 24 6W ]

[ 96 6W ]

Divide both sides by 6:

[ W 16 ]

Step 6: Find the Length

Now that we have the width, we can find the length using the expression ( L 12 2W ):

[ L 12 2(16) ]

[ L 12 32 ]

[ L 44 ]

Step 7: Verify the Solution

Let's check the solution by substituting ( W 16 ) and ( L 44 ) back into the perimeter equation:

[ 120 2(44) 2(16) ]

[ 120 88 32 ]

[ 120 120 ]

The solution satisfies the perimeter equation.

Conclusion

The dimensions of the rectangular swimming pool are 44 feet in length and 16 feet in width. By solving the algebraic problem, we have successfully determined the dimensions of the pool.

Additional Insights

Understanding the dimensions of your swimming pool can help you plan for additional tasks such as:

Calculating the volume of water needed.

Choosing the right size for pool accessories and equipment, such as filters and heaters.

Planning the landscaping and patio areas around the pool space.

Related Keywords

swimming pool dimensions, pool perimeter, algebraic equations