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? ... ?

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) = 15362x^2 - 24x + 64

= 384x^2 - 12x + 32

= 192x^2 - 12x - 160

= 0 (x - 20) (x + 8)

= 0x

= 202x

= 40

check: 12 * 32 * 4

= 1536