Let $G$ be any convex region tightly sandwiched between parallel lines $l_{1}$ and $l_{2}$ (i.e., the line segment connecting any two points on its boundary is contained within its region), and its boundary $C$ intersects with $l_{1}$ and $l_{2}$.
Parallel to $l_{1}$, the line $l$ divides $G$ into two parts $A$ and $B$ as shown in the figure, and the distances between $l$ and $l_{1}$ and $l_{2}$ are $a$ and $b$, respectively.
(1) What shape should $G$ be for the ratio of the areas of $A$ and $B$, $\frac{S_{\mathrm{A}}}{S_{\mathrm{B}}}$, to reach its maximum? Explain your reasoning;
(2) Try to find the maximum value of $\frac{S_{\mathrm{A}}}{S_{\mathrm{B}}}$.
(1) When $G$ is a triangle with one side on $l_{1}$ and another vertex on $l_{2}$, $S_{\mathrm{A}} / S_{\mathrm{a}}$ reaches its maximum.
(2) The maximum value of $S_{A} / S_{B}$ is $\frac{a^{2}+2 a b}{b^{2}}$.