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A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding up the sides. If the volume of the box will be 110 inches cubed what are the dimensions of the piece of cardboard?

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  1. Let x = width of cardboard
    Therefore L = x+6
    volume of open box is 110 in^3
    cut squares are 2 inches = H

    V=HXWxL=110
    H=2
    W=x-4
    L=(x+6)-4

    2(x-4)(x+2)=110 ==> divide both sides by 2

    (x-4)(x+2)=55
    x^2 -2x -8 = 55 ==> subtract 55 from both sides

    X^2 -2x -63 = 0 ==> factor

    (x-9)(x+7) = 0
    x= 9 or -7 ==> x has to be greater than 0, therefore answer is 9

    check

    2((9)-4)((9)+6-4)=110
    2(5)(11)=110
    110=110 it checks

    dimensions of cardboard is
    W=9 inches
    L=(9)+6=15 inches

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