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A rectangular piece of metal is 15 in longer than it is wide. Squares with sides

3 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1350 in3​, what were the original dimensions of the piece of​ metal?

User Uni
by
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1 Answer

3 votes

Let the width be
w inches and the length be
w+15 inches.

So, the dimensions of the box are
w-6,
w+9, and
3 inches.


3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21

Rejecting the negative case,
w=21.

So, the dimensions are 21 by 36 inches.

User Erik Johansson
by
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