Question

A rectangular piece of metal is 10 in longer than it is wide. Squares will side 2 in long are cut from the four corners and the flaps are fielded upward to form an open box. If the volume of the box is 1008 in^3, what were the original dimensions of the piece of mental

Answers

  1. The original dimensions of the piece of metal are; 22 inches is the width of the rectangular metal and 32 inches is the length.

    How to Maximize Volume?

    Let x = the width of the rectangular piece of metal
    then
    (x + 10) = the length
    Removing the 2 inches squares would make the dimensions of the box:
    (x – 4) by (x + 10-4) or (x – 4) by (x + 6)
    The height of the box = 2 inches
    The volume equation is; V = L * W * h
    Thus;
    (x + 6) * (x – 4) * 2 = 1008
    divide both sides by 2
    (x + 6)(x – 4) = 504
    FOIL
    x² – 4x + 6x – 24 = 504
    x² + 2x – 24 – 504 = 0
    x² + 2x – 528 = 0
    Using quadratic equation calculator, this will factor to
    (x + 24)(x – 22) = 0
    We will pick the positive solution;
    x = 22 inches is the width of the rectangular metal
    then
    32 inches = the length
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