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This is because 36 is a composite number.

A Prime number, p, has only the factorisation 1*p and so that is the only rectangle possible. But for a composite number there is at least one other factor q which may have a factor pair q' such that q*q' = p. q and q' could be the same if the number p was the square of q.


So then you have rectangles of size 1*p and q*q'.



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9y ago
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9y ago

ANY two positive numbers with a product of 36 will work. So, you can choose ANY real number (greater than zero), and then divide 36 by that number to get the other number.

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Q: Why is it possible to draw more than two different rectangles with an area of 36 units?
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