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A rectangular piece of cardboard is 2 units longer than it is wide?
From each of its corner a square piece 2 units on a side is cut out.The flaps are then turned up to form an open box that has a volume of 70 cubic units.Find the length and width of the original piece of cardboard.

  • algebra -

    Did you make a sketch?

    width of cardboard --- x
    length of cardboard -- x+2

    width of box = x-4
    length of box = x-2
    height of box = x

    volume = x(x-2)(x-4) = 70
    x^3 - 6x^2 + 8x - 70 = 0

    That was easy so far, but now we have a nasty cubic.
    I tried factors of 70 , no luck
    so I used Wolfram to find
    x = appr 6.4442

    original widht = 6.442
    original length = 8.442

    http://www.wolframalpha.com/input/?i=x%5E3+-+6x%5E2+%2B+8x+-+70+%3D+0

    check:

    original widht = 6.442
    original length = 8.442

    box base is 2.4442 by 4.4442

    volume = 2.4442 x 4.4442 x 6.4442 = 70.00002 , not bad

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