Azeneth is putting a fence around her rectangular garden. The width of the garden is 4x + 5 ft. and the

length is 2x^2 - 3x + 7 ft.

How much total fencing does Azeneth need to buy in terms of x?

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