2 Given 12 bamboo poles, each 13 units long, divide them into smaller segments of lengths 3, 4, or 5, and then assemble them into 13 triangles with side lengths of 3, 4, or 5. How should they be divided? Please explain your reasoning.
2. First, find the non-negative integer solutions of $3 a+4 b+5 c=13$. It is known that the lengths obtained after each bamboo stick is divided can only be $(3,3,3,4),(3,5,5),(4,4,5)$, a total of 3 cases. Then, let the number of times each case occurs be $x, y, z$, respectively, so we need to solve
$$\left\{\begin{array}{l}
3 x+y=13 \\
x+2 z=13 \\
2 y+z=13
\end{array}\right.$$

Solving this, we get
$$(x, y, z)=(3,4,5)$$

This means there are 3 bamboo sticks divided into $(3,3,3,4)$; 4 bamboo sticks divided into $(3,5,5)$; and another 5 bamboo sticks divided into $(4,4,5)$.