5. One side of a certain triangle is twice as large as another, and the perimeter of this triangle is 56. The quadrupled smallest side is 21 units longer than the largest side. Find the sides of this triangle.
Answer: 11, 22, 23.

Solution: A similar solution to this problem is present in Variant 1 under the same number.

Remark: 1 point for a correct solution found by trial and error.

Evaluation criteria are provided in the table:

| Points | $\quad$ Evaluation Criteria |
| :---: | :--- |
| $\mathbf{7}$ | Fully justified solution. |
| $\mathbf{6}$ | Justified solution with minor flaws. |
| $\mathbf{5 - 6}$ | The solution contains minor errors, gaps in justification, but is generally correct and can become fully correct after minor corrections or additions. |
| $\mathbf{4}$ | The problem is more solved than not, for example, one of two (more complex) significant cases is correctly considered. |
| $\mathbf{2 - 3}$ | The problem is not solved, but formulas, diagrams, considerations, or auxiliary statements relevant to the solution of the problem are provided. |
| $\mathbf{1}$ | The problem is not solved, but an attempt at a solution has been made, for example, individual (partial) cases have been considered in the absence of a solution or with an incorrect solution. |
| $\mathbf{0}$ | The solution is absent, or the solution does not meet any of the criteria listed above. |

Drawings and graphs for the problems.

8th grade. Problem 4.

![](https://cdn.mathpix.com/cropped/2024_05_06_d98cc5c45a098ce14162g-6.jpg?height=622&width=1310&top_left_y=503&top_left_x=430)

Fig. 1

9th grade. Problem 5.

![](https://cdn.mathpix.com/cropped/2024_05_06_d98cc5c45a098ce14162g-6.jpg?height=557&width=548&top_left_y=1523&top_left_x=503)

Fig. 2

![](https://cdn.mathpix.com/cropped/2024_05_06_d98cc5c45a098ce14162g-6.jpg?height=565&width=511&top_left_y=1505&top_left_x=1229)

Fig. 3