The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Verified step by step guidance

1. Define variables: Let the width of the pool be \(w\) meters. Then, the length of the pool is \$2w - 6$ meters, since it is 6 meters less than twice the width.
2. Recall the formula for the perimeter of a rectangle: \(P = 2 \times (\text{length} + \text{width})\). Here, the perimeter \(P\) is given as 126 meters.
3. Set up the equation using the perimeter formula: \$126 = 2 \times ((2w - 6) + w)$.
4. Simplify the equation inside the parentheses: \$126 = 2 \times (3w - 6)\(, then distribute the 2: \)126 = 6w - 12$.
5. Solve the linear equation for \(w\): add 12 to both sides to get \$126 + 12 = 6w\(, then divide both sides by 6 to find \)w\(. Once \)w\( is found, substitute back to find the length \)2w - 6$.

Key Concepts

Formulating Algebraic Expressions from Word Problems

This involves translating verbal descriptions into mathematical expressions or equations. For example, 'length is 6 meters less than twice the width' can be written as L = 2W - 6. This step is crucial for setting up equations that represent the problem.

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around it, calculated as P = 2(length + width). Understanding this formula allows you to relate the given perimeter to the dimensions of the pool and form an equation to solve.

Solving Linear Equations

Once the problem is expressed as an equation, solving linear equations involves isolating the variable to find its value. This includes combining like terms, using inverse operations, and checking solutions for accuracy.