1. A triangle has three sides of integer lengths, with the longest side being 11. The number of such triangles is ( ).
A. 32
B. 34
C. 36
D. 40
1. C Let the three sides of a triangle be integers $x, y, z$, and $x \leqslant y \leqslant z$, then $z=11, x+y \geqslant 12, x \leqslant y \leqslant 11$. Therefore, we only need to find the number of integer points within the triangle (including the boundary) formed by the lines $y=12-x, y=11, y=x$. It is easy to calculate that the number of integer points sought is 36.