7.4. Lena has two triangles and a quadrilateral, and Vasya has two triangles (different from Lena's) and a pentagon (all figures are cut out of a sheet of plywood). Both claim that they can form both a $4 \times 6$ rectangle and a $3 \times 8$ rectangle from their figures.

a) Could it be that Lena is right?

b) Could it be that Vasya is right?
Solution: a) Lena can be right. b) Vasya can also be right. Possible constructions are shown in the figure.
![](https://cdn.mathpix.com/cropped/2024_05_06_af3dcda7d9e478c75858g-6.jpg?height=614&width=1350&top_left_y=667&top_left_x=228)

Lena's construction

![](https://cdn.mathpix.com/cropped/2024_05_06_af3dcda7d9e478c75858g-6.jpg?height=234&width=603&top_left_y=1045&top_left_x=1115)

Vasya's construction

To the solution of problem 7.4

Answer: Both can be right.

Recommendations for checking:

| is in the work | points |
| :--- | :--- |
| Both constructions (Lena's and Vasya's) are provided. | 7 points |
| Only Vasya's construction is provided | 4 points |
| Only Lena's construction is provided | 3 points |
| Answer without justification and/or incorrect answer | 0 points |
| If the correct set of polygons is provided but it is not shown how they form a rectangle | -1 point for each rectangle |