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An infinite amount. You need to specify down to what decimal point.

I.e. 4+3.5+4+3.5 = 15, area = 14cm^2.

4.000001+3.499999+4.000001+3.499999=15, area = 13.9999995cm^2

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Q: How many rectangles can you draw with a fixed perimeter of 15 cm but having each one a different area?
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