Problem 4. Mira had a rectangular cardboard with sides $55 \mathrm{~cm}$ and $20 \mathrm{~cm}$. She divided it into squares with a perimeter of $20 \mathrm{~cm}$. How many squares did Mira get?
Solution. The perimeter of the small squares is $L=20 \mathrm{~cm}$. If the side of the small square is $a$, then from the equation $4 a=20$, we get $a=5 \mathrm{~cm}$.

The side with a length of $55 \mathrm{~cm}$ of the rectangular cardboard can be divided into 55:5=11 parts with a length of $5 \mathrm{~cm}$. The side with a length of $20 \mathrm{~cm}$ can be divided into $20: 5=4$ parts with a length of $5 \mathrm{~cm}$. Therefore, the rectangular cardboard with sides $55 \mathrm{~cm}$ and $20 \mathrm{~cm}$ can be divided into $11 \cdot 4=44$ square pieces with a perimeter of $20 \mathrm{~cm}$. Thus, Miro received 44 square pieces.