Expert: Sherry Wallin - 12/21/2009

Question
A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 unit on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard.

Answer
Hi William~
    Initially the length of the cardboard is w+2 and the width is w. When you removed the square pieces from each corner you are shortening both the width and the length by 4 units so now the 'box' is w-2 in length and w-4 in width. Since the squares removed are 2x2 that means the height of the box is going to be 2 so you have for volume of the box 2(w-4)(w-2) = 70 -> (w-4)(w-2) = 35 ->
w^2 - 6w + 8 = 35 -> w^2 - 6w - 27 = 0 -> (w+3)(w-9) = 0 -> w = 9 because width won't be negative like in -3. So w is 9 and l is w+2 = 11. Thus the original dimensions of the box are 9 units by 11 units.

Math Prof