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. Let the width of the pool be denoted as \( w \).
2. The length of the pool is 6 meters less than twice the width, so express the length as \( 2w - 6 \).
3. The formula for the perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width.
4. Substitute the given perimeter and the expressions for length and width into the perimeter formula: \( 126 = 2((2w - 6) + w) \).
5. Simplify and solve the equation for \( w \) to find the width, then use \( l = 2w - 6 \) to find the length.

Key Concepts

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around it, calculated by the formula P = 2(length + width). Understanding this formula is essential for solving problems related to the dimensions of rectangular shapes, as it relates the length and width directly to the perimeter.

Algebraic Expressions

Algebraic expressions involve variables and constants combined using mathematical operations. In this problem, we need to express the length in terms of the width using the relationship given (length = 2(width) - 6), which is crucial for setting up equations to find the dimensions of the pool.

Solving Linear Equations

Solving linear equations involves finding the value of variables that satisfy the equation. In this context, once we set up the equation based on the perimeter and the relationship between length and width, we can solve for the unknowns, leading us to the dimensions of the pool.