You have a 60-foot roll of fencing and a large field. You want to make two paddocks by continuing the fencing down the middle of a rectangul

Question

You have a 60-foot roll of fencing and a large field. You want to make two paddocks by continuing the fencing down the middle of a rectangular enclosure. What are the dimensions of the largest such enclosure you can make?

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Eirian 3 years 2021-08-18T13:55:57+00:00 1 Answers 0 views 0

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  1. thienan
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    2021-08-18T13:57:28+00:00
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    Answer:

    The dimension of the largest enclosure is width=10ft and length = 15ft

    Explanation:

    Let the width of the enclosure = a

    Let the length of the enclosure = L

    Let the area of the enclosure = A

    3w + 2l = 60 …eq1

    A = we …eq2

    From eq1

    2l = 60 – 3w

    Put 2l = 60 – 3w in eq2

    A = w(60 – 3w)/2

    A = w(30 – (3/2)w^2

    If A =0 , find the roots.

    The maximum will be?

    -b/2a this is exactly halfway between the roots

    -(3/2)w^2 + 30w =0

    -b = -30

    2a = -(3/2)

    -b/2a = -30/-3

    w = 10ft

    Put w = 10ft in eq 1

    3(10) + 2l = 60

    30 + 2l = 60

    2l = 60 – 30

    l = 30/2

    l = 15ft

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