Adam wants to create a square garden with a walkway on all four sides. The width of the walkway is 4 feet.
Write a function to represent the area of the garden in terms of the length of one side of the walkway, x. ???
If the walkway has outside length of x, the inside length (the side of the garden) is x-8
SO, the garden has area (x-8)^2
To find the area of the garden, we first need to calculate the area of the square without the walkway, and then subtract the area of the walkway.
Let's break down the problem:
1. Calculate the area of the square without the walkway:
The length of one side of the garden without the walkway will be (x - 2 * 4), as we need to subtract 4 feet from each side to account for the walkway. Therefore, the area of the garden without the walkway is (x - 2 * 4)^2.
2. Calculate the area of the walkway:
The walkway surrounds the garden on all four sides. So, the overall width of the garden, including the walkway, will be (x + 2 * 4). The area of the walkway around the garden is the difference between the area of the garden with the walkway and the area of the garden without the walkway. Thus, the area of the walkway is [(x + 2 * 4)^2 - (x - 2 * 4)^2].
3. Calculate the area of the garden:
Finally, to find the area of the garden, we subtract the area of the walkway from the area of the garden with the walkway. Therefore, the area of the garden is [(x + 2 * 4)^2 - (x - 2 * 4)^2] - (x + 2 * 4)^2.
Here's the function in mathematical notation:
Area of the garden = [(x + 2 * 4)^2 - (x - 2 * 4)^2] - (x + 2 * 4)^2