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23 November, 23:39

Aidan has 20 ft of fence with which to build a rectangular dog run. What is the maximum area he can enclose? Enter your answer in the box.

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  1. 24 November, 00:20
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    Maximum area is 25 m²

    Explanation:

    Let L be the length and W be the width.

    Aidan has 20 ft of fence with which to build a rectangular dog run.

    Fencing = 2L + 2W = 20 ft

    L + W = 10

    W = 10 - L

    We need to find what is the largest area that can be enclosed.

    Area = Length x Width

    A = LW

    A = L x (10-L) = 10 L - L²

    For maximum area differential is zero

    So we have

    dA = 0

    10 - 2 L = 0

    L = 5 m

    W = 10 - 5 = 5 m

    Area = 5 x 5 = 25 m²

    Maximum area is 25 m²
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