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25 February, 16:31

The width of a box is two inches less than twice the height. The length is 4 inches less than three times the height. The volume is 2240 cubic inches. What are the dimensions of the box

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  1. 25 February, 17:11
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    Dimensions are 8 Inches by 14 inches by 20 inches

    Step-by-step explanation:

    The volume of the box is 2240. This means:

    lbh = 2240

    Where b is the width.

    Width is two inches less than twice the height

    b = 2h - 2

    length is 4 inches less than 3 times the height

    l = 3h - 4

    Substituting these parameters into the lbh equation will yield the following:

    h * (3h - 4) * (2h - 2) = 2240

    h[6h^2-14h+8] = 2240

    6h^3 - 14h^2 + 8h - 2240 = 0

    Solving this cubic equation will yield one of the values to be 8. The other two values are complex numbers.

    b = 2h - 2

    l = 3h - 4

    b = 2 (8) - 2 = 14

    l = 3 (8) - 4 = 20
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