$17 \cdot 150$ The perimeter of a right triangle is $2+\sqrt{6}$, and the median to the hypotenuse is 1. Then the area of this triangle is 
(A) 1 .
(B) 2 .
(C) 4 .
(D) $\frac{1}{2}$.
(China Jilin Province Seven Cities and Prefectures Junior High School Mathematics Competition, 1987)
[Solution] From the given, we know the hypotenuse length is 2. As shown in the figure, we have
$$
\left\{\begin{array}{l}
a+b+c=2+\sqrt{6}, \\
a^{2}+b^{2}=c^{2},
\end{array}\right.
$$

From (1) and $c=2$, we have $a+b=\sqrt{6}$, then
$$
a^{2}+b^{2}+2 a b=6 \text {, }
$$

we have $\quad a b=1 . \quad \therefore \quad S_{\triangle}=\frac{1}{2} a b=\frac{1}{2}$.
Therefore, the answer is $(D)$.