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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:** \( P = 107 \)

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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!

Use the side lengths below to find the perimeter for each triangle when x = 10.
10. 3x + 1, x - 5, 6x - 4
11. 5x + 4, 2x + 3, x - 5
12. 2x + 7, x - 8, 9x - 12

Learn how to calculate the perimeter of triangles with algebraic expressions for side lengths, evaluated at x = 10. This example involves expressions such as 3x + 1, x - 5, and 6x - 4. The problem is suitable for students in Grades 7-9 and includes detailed solutions.

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