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A piece of machinery produces rectangular sheets of metal such that the length
is three times the width. Equal sized squares 5 cm on a side are removed from each corner
so that the resulting piece of metal can be shaped into an open box by folding up the flaps.
The volume of the box is to be 1435 cm3. What are the dimensions of the box?
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Let the width be x cm;
then the length is 3x cm, according to the condition.
After cutting squares and folding the flaps, the base of the box has dimensions of
(x-2*5) = x-10 cm and 3x-10 cm, so the volume equation is
5(x-10)*(3x-10) = 1435 cm^3, or
(x-10)*(3x-10) = 287.
Reduce to the standard quadratic form
3x^2 - 40x - 187 = 0
and find the roots via the quadratic formula. Choose the positive root, which is x = 17.
ANSWER. The dimensions of the box are 17-10 = 7 cm (the width) and 3*17-10 = 41 cm (the length).
CHECK the volume of the box is 7*41*5 = 1435 cm^3. ! Correct !
Solved.
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