A4. A square paper ring has height 1. The sides have length 4. The ring is depicted in the left figure. By pressing it flat on a table, we get the right figure. In this figure, quadrilateral $A B C D$ is a square.
![](https://cdn.mathpix.com/cropped/2024_04_17_9e808ca4ac6657f5611fg-2.jpg?height=272&width=990&top_left_y=366&top_left_x=503)

How long is side $A B$?
A) $\frac{5}{2}$
B) 3
C) $\frac{7}{2}$
D) 4
E) $\frac{9}{2}$
A4. B) 3 We look at the top edge of the paper ring. This edge has a length of $4 \times 4=16$. In the folded figure, the top edge follows the rectangle $E F G H$. Since $|A E|=|B F|=|C G|=$ $|D H|=1$, we see that $|A B|+|F G|+|C D|+|E H|=16-4=12$. These four lengths are equal to the lengths of the sides of the square $A B C D$. The sides of the square thus have a length of $\frac{12}{4}=3$.
![](https://cdn.mathpix.com/cropped/2024_04_17_8a1f196dae4ba99bbc23g-1.jpg?height=332&width=970&top_left_y=2342&top_left_x=538)