H>12 and w>12 however p≤60
p=2(h+w) but give what we have above for h and w
p>48 so p must satisfy the solution set:
48<p≤60 and since p=2(h+w)
48<2(h+w)≤60
24<h+w≤30
So there are infinitely many solutions if h and w are not restricted to integer values...
(h,w) vary from (12,18) to (18,12) Note that neither endpoints exist, 12 because it is explicitly excluded and 18 because that would make the other dimension 12 which is excluded...
Now if you are just talking integer values, there are only:
(13,17),(14,16),(15,15),(16,14),(17,13)
