0
Infinitely many.
Select any number, W, such that 0 < W ≤ 15. Since numbers are infinitely dense, there are infinitely many possible values for W. Let L = 30 - W. Then W ≤ L so each choice of W leads to a unique pair (W, L).
Now, a rectangle with width W cm and length L cm has a perimeter of 2*(L+W) = 2*(30 - W + W) = 2*30 = 60 cm, as required.
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