Question

An art student is searching for a rectangular canvas to paint on. His professor requires that both the height and width of the canvas exceed 12 inches, but because of the lack of framing materials, the perimeter cannot exceed 60 inches. Which of the following systems correctly describe the possible lengths (l) and width (w) of the canvas?

Answer 1

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)