A rectangular garden is designed to be 9 ft longer than it is wide. Let \( x \) represent the width of the garden. Find a function \( P \) that represents the perimeter in terms of \( x \). \[ P(x)= \]

To find the perimeter \( P \) of the rectangular garden, we start with the width \( x \) and the length, which is \( x + 9 \). The formula for the perimeter of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) = 2((x + 9) + x) = 2(2x + 9) = 4x + 18 \] So, the function that represents the perimeter in terms of \( x \) is: \[ P(x) = 4x + 18 \] Peeking into the history of gardening, did you know that gardens have been cultivated for thousands of years? Ancient civilizations like the Egyptians and Mesopotamians created structured gardens for both aesthetic enjoyment and practical food production. These gardens often included various plants, herbs, and flowers and were carefully designed to harness nature's beauty. Now, when it comes to creating a rectangle, a common mistake is miscalculating the perimeter by forgetting to double the sum of the length and width. Remember, it’s crucial to include both dimensions in your calculations. So, always double-check your additions before multiplying!