A house has a backyard with a square fire pit with side length

Question

feet, surrounded by two rows of 1-foot square stones.

The house also has a rectangular patio area where the length is 8 more feet than the width,
. The patio is surrounded with 4-foot square stones.

Multiple Choice Question
Which expression represents the perimeter of the rectangular patio?

Answer 1

To represent the perimeter of the rectangular patio, we first need to express the dimensions of the patio based on the given information.

Let the width of the patio be denoted as \( w \) feet. According to the problem, the length of the patio is \( w + 8 \) feet.

Now, the formula for the perimeter \( P \) of a rectangle is given by:

\[ P = 2(\text{length} + \text{width}) \]

Substituting the dimensions of the patio into the formula:

\[ P = 2((w + 8) + w) \]

Simplifying this expression:

\[ P = 2(2w + 8) \] \[ P = 4w + 16 \]

Thus, the expression that represents the perimeter of the rectangular patio is:

\(\boxed{4w + 16}\)