The perimeter of a rectangle is 24 inches, and its length is 3 times its width. What are the length and the width of the rectangle?

<h2>Question:</h2>

The perimeter of a rectangle is 24 inches, and its length is 3 times its width. What are the length and the width of the rectangle?

<h2>Choices:</h2>

• Length: 6 inches, Width: 2 inches

• Length: 9 inches, Width: 3 inches

• Length: 12 inches, Width: 4 inches

• Length: 18 inches, Width: 6 inches

<h2>Correct Answer:</h2>

Length: 9 inches, Width: 3 inches

<h2>Explanation:</h2>

To explain why the correct answer is "Length: 9 inches, Width: 3 inches," we need to use the given information about the rectangle and apply the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by the following formula:

\[ P = 2L + 2W \]

Here, \( L \) is the length, and \( W \) is the width. In the question, it is given that:

• The perimeter \( P \) is 24 inches.

• The length \( L \) is 3 times the width \( W \), which can be written as \( L = 3W \).

Substituting the value of \( L \) in the perimeter formula:

\[ P = 2(3W) + 2W \]

Simplify the equation:

\[ 24 = 6W + 2W \]

\[ 24 = 8W \]

Solving for \( W \):

\[ W = \frac{24}{8} = 3 \]

So, the width \( W \) is 3 inches. Since the length \( L \) is 3 times the width:

\[ L = 3 \times 3 = 9 \]

Therefore, the length \( L \) is 9 inches.

Thus, the correct dimensions of the rectangle are:

• Length: 9 inches

• Width: 3 inches

Therefore, the correct answer is indeed "Length: 9 inches, Width: 3 inches."