Answer:
Azeneth needs to buy 4x² + 2x + 24 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- Azeneth is putting a fence around her rectangular garden
- The width of the garden is 4x + 5 feet
- The length is 2x² – 3x + 7 feet
- We need to find how much total fencing Azeneth needs to buy in
terms of x
∵ The fence will put around the four sides of the rectangular garden
∴ The length of the fence is equal to the perimeter of the garden
- The perimeter of any rectangle = 2l + 2w, where l and w are its
dimensions
∵ The perimeter of the garden = 2 × its width + 2 × its length
∵ Width = 4x + 5
∴ 2 × width = 2(4x + 5) = 8x + 10
∵ Length = 2x² - 3x + 7
∴ 2 × length = 2(2x² - 3x + 7) = 4x² - 6x + 14
∴ The perimeter of the garden = 8x + 10 + 4x² - 6x + 14
- Add like terms
∴ The perimeter of the garden = 4x² + (8x - 6x) + (10 + 14)
∴ The perimeter of the garden = 4x² + 2x + 24
∵ The length of the fence = the perimeter of the garden
∴ The length of the fence = 4x² + 2x + 24 feet
* Azeneth needs to buy 4x² + 2x + 24 feet
