$32 \cdot 55$ Let the lengths of the sides of a scalene triangle (all sides are unequal) be integers, and the perimeter is less than 13. Then, the number of such triangles is
(A) 1 .
(B) 2 .
(C) 3 .
(D) 4 .
(China Beijing Junior High School Mathematics Competition, 1991)
[Solution] Let the three sides of the triangle be $a, b, c$, and $a<b<c$. According to the problem, we have $a+b+c<13$, and $a, b, c \in N$. Thus,
when $a+b+c=12$, $a=3, b=4, c=5$;
when $a+b+c=11$, $a=2, b=4, c=5$;
when $a+b+c=10$, there is no solution that fits the problem;
when $a+b+c=9$, $a=2, b=3, c=4$.
when $a+b+c \leqslant 8$, there is no solution that fits the problem.
Therefore, the answer is $(C)$.