6.4. A square (see figure) was cut into rectangles. It turned out that the areas of all six cut-off rectangles are equal to each other. Find how many times the long side of the shaded rectangle is greater than its short side. Justify your answer.
Solution: Since the areas of all hexagons are equal, the area of each is $1 / 6$ of the area of the square, so the three left rectangles make up half of the square. Therefore, the horizontal side of the shaded rectangle is also equal to half the side of the square. Since its area is $1 / 6$ of the area of the square, the other side is $1 / 3$ of the side of the square. Thus, the desired ratio is $1 / 2: 1 / 3 = 1.5$.

Answer: 1.5 times.

Recommendations for checking:

| included in the work | points |
| :--- | :--- |
| correct and fully justified answer | 7 points |
| an incorrect answer due solely to arithmetic errors | 6 points |
| specific dimensions of the square and obtained rectangles are provided without proof of the uniqueness of the picture (up to similarity) | 4 points |
| the ratio of one side of the shaded rectangle to the side of the square is correctly found | 3 points |
| only the correct answer is provided without justification (or with incorrect justification) | 1 point |