$25 \cdot 25$ If $a, b>0$, the line $a x+b y=6$ and the coordinate axes form a triangle in the first quadrant with an area of 6, then $a b$ equals
(A) 3 .
(B) 6 .
(C) 12 .
(D) 108 .
(E) 432 .
(40th American High School Mathematics Examination, 1989)
[Solution] As shown in the figure, the intersection points of the line with the two coordinate axes are

then
$$
\begin{array}{c}
\left(\frac{6}{a}, 0\right) \text { and }\left(0, \frac{6}{b}\right), \\
S_{\triangle}=\frac{1}{2} \cdot \frac{6}{a} \cdot \frac{6}{b}=6 .
\end{array}
$$

Therefore,
$$
a b=3 \text {. }
$$

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