The perimeter of a rectangle is 22 inches and the inch measure of each side is a natural number how many different areas in square inches can the rectandgl have why?

Suppose the rectangle has length L and width W where, as per convention, L >= W.

Now Perimeter = 22 = 2(L+W) so L+W = 11

L is a whole number >=11/2 ie L >= 6

Also, W>0 so L <= 10.

Thus L = 6,7,8,9,10 giving 5 possible areas for the rectangle.