2.1 Two squares are arranged as shown in the figure. If the part of the smaller square that intersects with the larger one is cut off, 52% of its area will remain, and for the larger square, without their common part, 73% of its area will remain. Find the ratio of the side of the smaller square to the side of the larger one.

![](https://cdn.mathpix.com/cropped/2024_05_06_6a9b962ccc5e03d35f9eg-03.jpg?height=394&width=420&top_left_y=520&top_left_x=835)
Answer: 0.75

Solution. Note that $27\%$ of the area of the larger square is equal to $48\%$ of the area of the smaller square, that is, the ratio of the areas is $\frac{27}{48}=\frac{9}{16}$. But the area of each square is equal to the square of the ratio of the sides, so the sides are in the ratio $3 \div 4=0.75$.