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Math Help - Polynomial Story Problem

  1. #1
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    Polynomial Story Problem

    As part of a landscaping project, you put in a flower bed measuring 10 feet by 12 feet. You plan to surround the bed with a uniform border of low-growing plants.

    Write a polynomial that describes the area of the uniform border that surrounds the bed. Explain what you did and why.

    The low-growing plants surrounding the flower bed require 1 sq. foot each when mature. If you have 168 of these plants, how wide a strip around the bed should you prepare the border? Explain what you did and why.

    If someone can help me set up the problem, I can figure out how to solve it.
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  2. #2
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    Hello, mjfaris!

    Did you make a sketch?


    You put in a flower bed measuring 10 feet by 12 feet.
    You plan to surround the bed with a uniform border of low-growing plants.

    (a) Write a polynomial that describes the area of the uniform border that surrounds the bed.
    Explain what you did and why.

    (b) The plants in the border require 1 ft² each when mature.
    If you have 168 of these plants, how wide should the border be?
    Code:
          : x :    12    : x :
        - * - - -  - - - - - *
        x |                  |
        - |   * - -  - - *   |
          |   |    12    |   |
       10 |   |10        |   | 2x+10
          |   |          |   |
        - |   * - - -  - *   |
        x |                  |
        - * - - - - - -  - - *
                 2x+12

    The inner bed is 10-by-12 feet.
    . . Its area is: . 10\cdot12 \:=\:120 ft².

    The border is x feet wide.

    The length of the entire garden is: 2x+12 feet.
    The width of the entire garden is: 2x+10 feet.
    . . Its area is: . (2x+12)(2x+10) ft².


    \text{(Area of border)} \;=\;\text{(Area of entire garden)} - \text{(Area of inner bed)}

    So, we have: . A \;=\;(2x+12)(2x+10) - 120


    Can you finish it now?

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  3. #3
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    Thank you so much!
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  4. #4
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    Re: Polynomial Story Problem

    I understand how you got A. But, for the life of me I can not figure out B. This is also a problem for my algebra homework. Please help me!
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