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) = 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