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UKMT Senior Kangaroo, 2022

Geometry Difficulty 2.0 Junior Prove it United Kingdom

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 $\frac{360x}{y}$ ?

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