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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