Example: How many types of isosceles triangles with integer side lengths and a perimeter of 100 are there?
(8th "Hua Luogeng Cup" Junior Mathematics Invitational Final)
Let $a$, $b$, and $c$ be the lengths of the three sides of a triangle.
(1) $a=ba .\end{array}\right.$,
Solving, we get $25<a<33 \frac{1}{3}$.
Therefore, there are 8 possibilities.
(2) $a<b=c$.

In this case, $a=100-2 c$.
Thus, $\left\{\begin{array}{l}100-2 c<c \\ 1+2 c \leqslant 100\end{array}\right.$.
Solving, we get $33 \frac{1}{3}<c \leqslant 49 \frac{1}{2}$.
Therefore, there are 16 possibilities.
In total, there are 24 possibilities.