You have just bought a new puppy and want to fence in an area in the backyard for her to roam. You buy 100 linear feet from Home Depot and h

Question

You have just bought a new puppy and want to fence in an area in the backyard for her to roam. You buy 100 linear feet from Home Depot and have decided to make a rectangular fenced in area using the back of your house as a side. What are the dimensions to maximize the area your puppy can roam

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3 days 2021-07-20T04:55:46+00:00 1 Answers 1 views 0

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    2021-07-20T04:57:08+00:00

    Answer:

    50 ft * 25 ft

    Step-by-step explanation:

    Let the length of the rectangular area be x ft and the width of the rectangular area be y ft. You already have 100 ft of material for fencing. Also one side of your house is used in fencing.

    The perimeter of the fence needed = x + 2y

    Therefore:

    100 = x + 2y

    x = 100 – 2y

    Also the area of the rectangular fence is:

    Area (A) = length * breadth

    A = xy

    Substitute x = 100 – 2y

    A = (100 – 2y)y

    A = 100y – 2y²

    Maximum area is at dA / dy = 0. Hence:

    dA/dy = 100 – 4y

    100 – 4y = 0

    4y = 100

    y = 25 ft

    substitute value of y in x:

    x = 100 – 2y = 100 – 2(25) = 100 – 50 = 50 ft

    x = 50 ft

    The dimension of the rectangular space is 50 ft * 25 ft

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