$17 \cdot 61$ The perimeter of an isosceles triangle is 24, and a median to one of the equal sides divides the perimeter into two parts in the ratio $5: 3$. Then, the length of the base of the triangle is
(A) 7.5 .
(B) 12 .
(C) 4 .
(D) 12 or 4 .
(1st "Hope Cup" National Mathematics Invitational, 1990)
[Solution] Let the length of the legs of the triangle be $2x$, and the base be $y$. According to the problem, we have
$$
\left\{\begin{array}{l}
\frac{3 x}{x+y}=\frac{5}{3}, \\
4 x+y=24 ;
\end{array} \text { or } \left\{\begin{array}{l}
\frac{3 x}{x+y}=\frac{3}{5}, \\
4 x+y=24 .
\end{array}\right.\right.
$$
However, when $y=12$, it already accounts for half of the perimeter, which is not appropriate. Therefore, $y=4$. Hence, the correct choice is $(C)$.