Problem 4. Dimitar has two square cardboards with sides of $3 \mathrm{~cm}$ and $4 \mathrm{~cm}$. Can he, by cutting, form a square without discarding material? If the answer is affirmative, what is the side of that square?
Solution. Dimitar can form a square with a side length of $5 \mathrm{~cm}$. The square with a side of $3 \mathrm{~cm}$ will be divided into rectangles with sides 1 $\mathrm{cm}$ and $3 \mathrm{~cm}$, one rectangle with sides $1 \mathrm{~cm}$ and $2 \mathrm{~cm}$, and one square with a side of $1 \mathrm{~cm}$. He will add them to the square with a side of $4 \mathrm{~cm}$ as shown in the diagram.

Note. Other solutions are possible.
![](https://cdn.mathpix.com/cropped/2024_06_05_9d1696c7fd1a2cbf5bb5g-05.jpg?height=252&width=692&top_left_y=226&top_left_x=463)