# SOLUTION: What is the greatest number of rectangles with integer side lengths and perimeter 10 that can be cut from a piece of paper with width 24 and length 60? A)144 B)180 C)240 D)360

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 Click here to see ALL problems on Rectangles Question 611540: What is the greatest number of rectangles with integer side lengths and perimeter 10 that can be cut from a piece of paper with width 24 and length 60? A)144 B)180 C)240 D)360 E)480Answer by htmentor(789)   (Show Source): You can put this solution on YOUR website!The maximum number of rectangles will be obtained if the area of each cut rectangle is a minimum The perimeter of each cut rectangle = P = 2(l+w) = 20 -> l+w = 5 -> w = 5-l The area of each cut rectangle = A = l*w = l*(5-l) The possible values for l are 1,2,3 and 4, giving areas of 4, 6, 6 and 4 So l=4 gives the minimum area (letting the length be the longer dimension) Take the ratio of the areas to give the number of cut rectangles: 24*60/4 = 6*60 = 360 Ans: D