# SOLUTION: how would you solve a problem such as: A rectangular piece of cardboard is made into an open box (that is, it has no top) by cutting a 2-inch square from each corner and turning u

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 Question 353990: how would you solve a problem such as: A rectangular piece of cardboard is made into an open box (that is, it has no top) by cutting a 2-inch square from each corner and turning up the sides. If the original piece of cardboard (before the corners are cut out) has an area of 216 square inches and the completed box has a volume of 224 cubic inches, determine the dimensions of the piece of cardboard.Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!x * y = 216 2(x-4)(y-4) = 224 ___ (x-4)(y-4) = 112 ___ xy - 4x - 4y + 16 = 112 216 - 4x - 4y + 16 = 112 ___ 120 = 4x + 4y ___ 30 = x + y ___ 30 - x = y x(30-x) = 216 ___ 0 = x^2 - 30x + 216 factoring ___ 0 = (x - 18)(x - 12)