Question

A rectangular piece of metal is twice as long as it is wide. Squares with sides 4 inches long are cut from the four corners and the flaps are folded upward to form a box. If the volume is 1536 inches cubed, what were the original dimensions of the piece of metal?

Answer 1

original rectangle has sides x and 2x. the box will have length 2x - 8, width x - 8, and height 4. So the volume is length x width x height:
(2x - 8)(x - 8)(4) = 1536
2x^2 - 24x + 64 = 384
x^2 - 12x + 32 = 192
x^2 - 12x - 160 = 0
(x - 20)(x + 8) = 0
x = 20
2x = 40
check: 12 * 32 * 4 = 1536

Answer 2

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