MATH ANALYSIS

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How should this be done?


Suppose you have 132 m of fencing with which to make two side-by-side rectangular enclosures against an existing wall. if the rectangular enclosures are adjacent and of the same depth what is the maximum are that can be enclosed?

  • MATH ANALYSIS -

    Let the combined length of the two rectangles by y
    let the width be x (there will be 3 of those)

    so 3x + y = 132
    y = 132-3x

    Area = xy
    = x(132-x)
    = -x^2 + 132x

    by Calculus
    d(Area)/dx = -2x + 132 = 0 for a max of Area
    x = 66
    then max Area = 66(132-66) = 4356 m^2

    by completing the square:
    Area = -[x^2 - 132x + 4356 - 4356 ]
    = -(x-66)^2 + 4356

    so the max Area is 4356 , when x = 66

  • MATH ANALYSIS -

    thanks!

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