$17 \cdot 163$ The three sides of a triangle are $2, 3, 4$, and the angle bisector of the largest angle divides the original triangle into two smaller triangles. Then the ratio of the area of the smaller to the larger of the two smaller triangles is
(A) $4: 9$.
(B) $2: 3$.
(C) $1: 3$.
(D) $1: 2$.
("Jianghan Cup" Junior High School Mathematics Competition, 1991)
[Solution] As shown in the figure, then
$$
\begin{aligned}
& S_{\triangle A E C}: S_{\triangle A E B} \\
= & \left(\frac{1}{2} \cdot A C \cdot A E \cdot \sin \angle E A C\right):\left(\frac{1}{2} \cdot A B \cdot A E \cdot \sin \angle E A B\right) \\
= & A C: A B \\
= & 2: 3 .
\end{aligned}
$$

Therefore, the answer is $(B)$.