The width of a rectangle is 20 less than 3 times the length. If the perimeter is 32 ft, find its

The width of a rectangle is 20 less than 3 times the length....

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Key Concepts

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around the shape and is calculated by adding together twice the length and twice the width. This concept is essential in geometry and helps in formulating equations when certain measurements or relationships between the sides are known.

Translating Verbal Descriptions to Algebraic Expressions

This involves converting a word problem into mathematical expressions or equations. In problems where a dimension is described in relation to another (for example, one side being a certain amount more or less than a multiple of another), it is crucial to correctly interpret and express these relationships algebraically.

Setting Up Equations

By using the information provided in a problem, such as the relationship between sides and the total perimeter, one can set up an equation that represents the situation mathematically. This step typically involves substituting the expressed relationships into the formula for the perimeter or area.

Solving Linear Equations

Once the equation is set up, solving it usually involves techniques such as combining like terms, isolating the variable, and solving for the unknown. This step is an application of fundamental algebraic methods and is critical for determining the numerical values of the dimensions described in the problem.