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10 February, 18:27

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?

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Answers (1)
  1. 10 February, 18:55
    0
    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
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