54. A rectangular piece of cardboard is 2 units longer than itis wide. From each

Question

54. A rectangular piece of cardboard is 2 units longer than itis wide. From each of its corners a square piece 2 units on a sideis cut out. The flaps are then turned up to form an open box thathas a volume of 70 cubic units. Find the length and width of theoriginal piece of cardboard.

Explanation / Answer

54.    Initially the length of the cardboard is w+2 andthe width is w. When you removed the square pieces from each corneryou are shortening both the width and the length by 4 units so nowthe 'box' is w-2 in length and w-4 in width. Since the squaresremoved are 2x2 that means the height of the box is going to be 2so 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 9and l is w+2 = 11. Thus the original dimensions of the box are 9units by 11 units. 66. 54=(n^2-3n)/2 108=n^2-3n 0=n^2-3n-108 (n-12)(n+9)=0 n=12

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