A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1536 in. cubed find the length and width of the original piece of metal.

Suppose:

width=x in

length=2x-6

when 3 inches square is cut from the corner, the new dimensions will be:

width = (x-6) in

length = (2x-6-6) = (2x-12) in

height=3 in

thus the volume will be:

(x-6) (2x-12) 3=1536

solving the above we get:

x=-10 or x=22

thus the original:

width=22 in

length=22*2-6=38 in