The length of a rectangular garden, inn rectangle, is 9ft more than its width. For the garden, let x=width, x+9 = length. It is surrounded by a brick walkway 4 ft wide. Suppose the total area of the walkway is 400 ft.

Write a polynomial to represent the length of PQ

Step-by-step explanation:

Not sure what PQ is but I can get started witht he info. So we start with the rectangular garden. Then the brick walkway makes a larger rectangle, which is the walkway and the garden inside of it. If you took the area of this larger rectangle and then subtracted the area of the garden you would have the area of the walkway, which it says is 400, so we'll keep that in mind.

For the area of the garden we have the length and width, so it's x (x+9)

Factoring in the walkway, which is f feet wide, means that 4 feet is being added on both ends of the height length and width. so basically 4 + w + 4 for the width and 4 + l + 4 for length. Plugging in what length and width are we get 4 + x + 4 for width and 4 + (x + 9) + 4 for length. If we simplify by combining like terms we get 8 + x and 17 + x for width and length respectively. Now we can find the area of the larger rectangle. (8+x) (17+x)

Now, we may not know the area of the garden or the large rectangle, but we know their difference. Garden Area - Large Area = 400 or x (x+9) - (8+x) (17+x) = 400

From here you just expand to get a polynomial that would solve for x, which is the width of the garden, but can be used to find everything else.