  In this paper we first study the isoperimetric problem in the case of integer
triangles, as well as Alcuin's sequence and how it relates to the number of
different integer triangles with a given perimeter. We then present and compare
two different approaches to the above problem. The first approach is due to a
university professor (a working mathematician), who uses a well-known technique
of calculating the number of elements of finite sets, while the second one is
due to a high school student with a special interest in mathematics and is
purely number-theoretic. Furthermore, some related instructor perspectives are
discussed.

General Mathematics