Question 430037
No. Consider the (perimeter) function {{{p(x) = 2x + x*sqrt(2)}}} where x is the length of a leg. This is equivalent to {{{p(x) = x(2 + sqrt(2))}}} which is linear. The linear function is defined on all positive real numbers, and its range is all real numbers, including integers. Hence, it is possible for the perimeter to be an integer (for example, replace {{{x = 1/(2 + sqrt(2))}}} and you will find that the perimeter is 1).