$18 \cdot 66$ The base of a triangle is $b$, and its height is $h$. A rectangle is inscribed in the triangle, with its base on the base of the triangle, and its height is $x$. Then the area of the rectangle is 
(A) $\frac{b x}{h}(h-x)$.
(B) $\frac{h x}{b}(b-x)$.
(C) $\frac{b x}{h}(h-2 x)$.
(D) $x(b-x)$.
(E) $x(h-x)$.
(11th American High School Mathematics Examination, 1960)
[Solution] Let the length of the rectangle be $y$ (as shown in the figure). By the property of similar figures, we have
$$
\begin{aligned}
& \frac{h-x}{y}=\frac{h}{b}, \text { i.e., } y=\frac{b}{h}(h-x) . \\
\therefore \quad & S_{\text {rectangle }}=x y=\frac{b x}{h}(h-x) .
\end{aligned}
$$

Therefore, the correct choice is $(A)$.