The image contains problems asking to calculate the perimeter of triangles with given algebraic expressions for side lengths, evaluated at $x = 10$. I’ll solve each question in detail below:

Problem 10:

Side lengths:

• $3x + 1$
• $x - 5$
• $6x - 4$

Perimeter formula for a triangle: $P = \text{sum of all sides}.$ Substitute the side lengths: $P = (3x + 1) + (x - 5) + (6x - 4).$ Simplify: $P = 3x + x + 6x + 1 - 5 - 4 = 10x - 8.$ Substitute $x = 10$: $P = 10(10) - 8 = 100 - 8 = 92.$

Problem 11:

Side lengths:

• $5x + 4$
• $2x + 3$
• $x - 5$

Perimeter: $P = (5x + 4) + (2x + 3) + (x - 5).$ Simplify: $P = 5x + 2x + x + 4 + 3 - 5 = 8x + 2.$ Substitute $x = 10$: $P = 8(10) + 2 = 80 + 2 = 82.$

Problem 12:

Side lengths:

• $2x + 7$
• $x - 8$
• $9x - 12$

Perimeter: $P = (2x + 7) + (x - 8) + (9x - 12).$ Simplify: $P = 2x + x + 9x + 7 - 8 - 12 = 12x - 13.$ Substitute $x = 10$: $P = 12(10) - 13 = 120 - 13 = 107.$

Summary of Results:

1. Problem 10: $P = 92$
2. Problem 11: $P = 82$
3. Problem 12: $P = 107$

Do you want further details or have any questions? Here are related problems to explore:

1. What is the general formula for a triangle’s perimeter?
2. How do you verify the solution to these problems?
3. What happens if $x = 0$ in these equations?
4. How do expressions for perimeter relate to other geometric properties (e.g., area)?
5. Can these expressions model real-world situations?

Tip: Always double-check your substitutions to avoid arithmetic errors!