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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? ...?

Respuesta :

syed514
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

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