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Math Help - Polynomial Functions 1

  1. #1
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    Post Polynomial Functions 1

    A boardwalk that is x feet wide is built around a rectangular pond. The pond is 30 ft wide and 40 ft long. The combined surface area of the pond and the boardwalk is 2000 ft^2. What is the width of the boardwalk?

    I tried 2000^2 - (30*40) = 800ft^2 as the surface area of the boardwalk but I don't know if I was on the right track. How should I do this question?

    The answer is 5ft.
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  2. #2
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    Re: Polynomial Functions 1

    Quote Originally Posted by Mathnood768 View Post
    A boardwalk that is x feet wide is built around a rectangular pond. The pond is 30 ft wide and 40 ft long.

    So the board walk adds x feet to either side the pond and board walk form a rectangle with width 30+ 2x and length 40+ 2x feet.

    The combined surface area of the pond and the boardwalk is 2000 ft^2. What is the width of the boardwalk?
    A rectangle of length 30+ 2x feet and width 40+ 2x feet has area (30+ 2x)(40+ 2x)= 2000.

    I tried 2000^2 - (30*40) = 800ft^2 as the surface area of the boardwalk but I don't know if I was on the right track. How should I do this question?
    Yes, that is the surface area of the boardwalk (I believe you mean 2000 ft^2 rather than "2000^2")- you could then calculate the lengths of the four "sides" on the rectangle but the above is easier.

    The answer is 5ft.
    You could, for example, "dissect" the boardwalk as two rectangles of length 40 and width x and two rectangles of length 30+ x (draw a picture to see why) and width x so area 2(x)(40)+ 2(x)(30+ x)= 800. That give you the same equation as before.
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