14. The lengths of the sides of a triangle are the integers $13, x, y$. It is given that $x y=105$. What is the length of the perimeter of the triangle?
14. 35 Assume, without loss of generality, that $x \leqslant y$. Since $x, y$ are positive integers and $x y=105$, the possible values of $(x, y)$ are $(1,105),(3,35),(5,21),(7,15)$.
Since we require $13+x>y$ for the triangle to exist, we may eliminate the first three of these possibilities, leaving only $(7,15)$ and conclude that the perimeter is $13+7+15=35$.