A rectangle has a length of 14 cm and a width that is half of its length.What is its perimeter?

1. Break Down the Problem

To find the perimeter of the rectangle, we must first determine the width. The problem states that the width is half of the length. After calculating the width, we can use the perimeter formula for a rectangle.

2. Relevant Concepts

The formula for the perimeter $P$ of a rectangle is given by: $P = 2 \times (L + W)$ where $L$ is the length and $W$ is the width.

3. Analysis and Detail

1. Calculate the Width:

   • Given that the length $L = 14$ cm, the width $W$ can be calculated as: $W = \frac{L}{2} = \frac{14}{2} = 7 \text{ cm}$

2. Calculate the Perimeter:

   • Now, substituting the values of $L$ and $W$ into the perimeter formula: $P = 2 \times (14 + 7) = 2 \times 21 = 42 \text{ cm}$

4. Verify and Summarize

We confirmed that the length is 14 cm and the width is correctly calculated as 7 cm. Substituting these values into the perimeter formula yielded a result of 42 cm.

Final Answer

The perimeter of the rectangle is $42$ cm.