4. The rectangles $S_{1}$ and $S_{2}$ are drawn on a set of coordinate axes. $S_{1}$ has vertices at $(0, y) ;(x, y) ;(x, 4)$; and $(0,4)$, where $x<9$ and $y<4$. $S_{2}$ has vertices at $(x, 0)$; $(9,0) ;(9, y)$; and $(x, y)$. The rectangles are equal in area. What is the value of $\frac{360 x}{y}$ ?
Solution
810

Rectangles $S_{1}$ and $S_{2}$ have areas $x(4-y)$ and $y(9-x)$ respectively.
Equating these, $4 x-x y=9 y-x y$.
Therefore, $4 x=9 y$, which yields $360 x=810 y$ giving the result of $\frac{360 x}{y}=810$.