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 ?

Options

A. 2w + 6
B. 4w + 12
C. `w^2 + 6`
D. `w^2 + 6w`

Explanation

To find the perimeter of the rectangular dance floor in terms of its width \( w \), we can follow these steps:

### Step 1: Define the Width and Length
- The width of the dance floor is given as \( w \) feet.
- The length of the dance floor is stated to be 6 feet longer than its width. Therefore, we can express the length \( L \) as:
\[ L = w + 6 \]

### Step 2: Use the Perimeter Formula
- The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{Width} + \text{Length}) \]
- Substituting the expressions for width and length into the formula, we have:
\[ P = 2 \times (w + (w + 6)) \]

### Step 3: Simplify the Expression
- Now, simplify the expression inside the parentheses:
\[ P = 2 \times (w + w + 6) = 2 \times (2w + 6) \]
- Next, distribute the 2:
\[ P = 4w + 12 \]

### Final Expression
- Therefore, the perimeter of the dance floor in terms of \( w \) is:
\[ P = 4w + 12 \]