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Mathematics

A farmer needs to enclose three sides of a garden with a fence (the fourth side is a cliff wall). The farmer has 47 feet of fence and wants the garden to have an area of 266 sq-feet. What should the dimensions of the garden be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). Additionally, the length should be as long as possible.)

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  1. 2 w + L = 47
    w L = 266 so L = 266/w
    2 w + 266/w = 47
    2 w^2 - 47 w + 266 = 0
    (2w-19)(w-14) = 0
    w = 9.5 or w =14
    if the length is to be max, the width should be min so use w = 9.5
    L= 47 - 19 = 28

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