math

a 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard.the sides are folded up to make an open box with a maximum volume.if the perimeter of the base is 50cm,what are the dimensions of the box.

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  1. let the width of the base be x
    let the length of the base by y
    2x + 2y = 50
    x + y = 25 ---> y = 25-x

    volume = V = 5xy
    = 5x(25-x)
    = 125x - 5x^2
    dV/dx = 125 - 10x = 0 for a max of V
    10x = 125
    x = 12.5
    y = 12.5

    the box is 12.5 by 12.5 by 5 cm

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  2. I want the solution

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