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Open-top box. Thomas is going to make an open-top box
by cutting equal squares from the four corners of an
11 inch by 14 inch sheet of cardboard and folding up the
sides. If the area of the base is to be 80 square inches, then
what size square should be cut from each corner?

  • algebra -

    The parts cut out (x) have to be square or else the heights of the box won't match.
    The area of the base is to be 80 square inches.
    The lengths and sides are 11 and 14, therefore the dimensions of the base would be (11-2x) and (14-2x).
    We get the constraint / relationship:
    (11-2x)(14-2x) = 80
    Solve the quadratic equation for x.
    Unfortunately the equation does not factor, so you will need the quadratic formula to solve it. It should be between 1.5 and 2.

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