The width of a rectangular dance floor is w feet. The length...

The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of $w?$
A) $2 w+6$
B) $4 w+12$
C) $w^{2}+6$
D) $w^{2}+6 w$

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Key Concepts

Rectangle Properties

A rectangle is a quadrilateral with opposite sides that are equal in length and four right angles. This understanding is essential because many geometric problems involve computing properties like perimeter and area based on these characteristics.

Perimeter Formula for Rectangles

The perimeter of a rectangle is found by adding the lengths of all four sides, which simplifies to 2 times the sum of the length and the width (P = 2(l + w)). This formula is fundamental when expressing the perimeter in terms of given variables.

Algebraic Expression Setup

In problems where relationships are provided between dimensions, such as the length being a fixed amount longer than the width, it is crucial to translate this relationship into an algebraic expression. This allows the substitution of one variable into formulas like the perimeter formula.

Substitution into Formulas

Substitution is the process of replacing a variable with its given equivalent expression. When the length is given in terms of the width, such as length = width + 6, it can be directly substituted into the perimeter formula to create an expression solely in terms of the width.

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