II. (Full marks 14 points) Use 100 matchsticks of equal length to form a triangle, such that the length of the longest side is three times the length of the shortest side. Find the number of matchsticks used for each side of the triangle that meets this condition.

Use 100 matchsticks of equal length to form a triangle, such that the length of the longest side is three times the length of the shortest side. Find the number of matchsticks used for each side of the triangle that meets this condition.
Let the number of matchsticks required for each side of the triangle be $x, y, 3x$. According to the problem, we have
$$
\left\{\begin{array}{l}
x+y+3 x=100, \\
x \leqslant y \leqslant 3 x, \\
x+y<3 x .
\end{array}\right.
$$

From (1) and (2), we get $\frac{100}{7} \leqslant x \leqslant 20$, and from (3) we get $x<\frac{50}{3}$.
Since $x$ is a positive integer, $x$ can take the values 15 and 16.
Therefore, there are two sets of triangles that meet the conditions, with the number of matchsticks required being $15,40,45$ or $16,36,48$.