A rectangular piece of sheet metal has a length that is 4 in

A rectangular piece of sheet metal has a length that is 4 in less than twice the width. A square piece 2 in on a side is cut from each corner. The sides are then turned up to form an uncovered box of volume 256 in.3. Find the length and width of the original piece of metal.

Solution

length that is 4 in less than twice the width

Let length be l and width be w

So, l = 2w -4

A square piece 2 in on a side is cut from each corner and sides are then turned up to form an uncovered box

so, length = l -4 = 2w -4 -4 = 2w-8

width = w-4

Volume = l*w*2 = (2w-8)(w-4)*2 = 256.3

2w^2 -8w -8w +32 = 128.15

2w^2 -16w -96.15 =0

solve for w : w= 12 , -4 ( Neglect -ve root)

So, width w = 12inch ; l = 2w-4 = 20 inch