https://file.aiquickdraw.com/mathbot/file/1728498120650hw19g93v.jpg

Let's break down the triangles one by one to find their perimeters.

### 1. **Pink Triangle:**
Sides: \( x + 6 \), \( 3x - 2 \), and \( 2x + 4 \).

- **Perimeter formula:** Add all the sides.
  \[
  \text{Perimeter} = (x + 6) + (3x - 2) + (2x + 4)
  \]
  Simplifying:
  \[
  = x + 3x + 2x + 6 - 2 + 4
  = 6x + 8
  \]
  The perimeter of the pink triangle is \( 6x + 8 \).

---

### 2. **Yellow Triangle:**
Sides: \( 6x + 4 \), \( 7x - 1 \), and \( 5x + 7 \).

- **Perimeter formula:**
  \[
  \text{Perimeter} = (6x + 4) + (7x - 1) + (5x + 7)
  \]
  Simplifying:
  \[
  = 6x + 7x + 5x + 4 - 1 + 7
  = 18x + 10
  \]
  The perimeter of the yellow triangle is \( 18x + 10 \).

---

### 3. **Green Triangle:**
Sides: \( 4x - 3 \), \( 3x \), and \( 5x - 6 \).

- **Perimeter formula:**
  \[
  \text{Perimeter} = (4x - 3) + 3x + (5x - 6)
  \]
  Simplifying:
  \[
  = 4x + 3x + 5x - 3 - 6
  = 12x - 9
  \]
  The perimeter of the green triangle is \( 12x - 9 \).

---

### 4. **Blue Triangle:**
Sides: \( 6x - 8 \), \( 3x + 7 \), and \( 5x - 3 \).

- **Perimeter formula:**
  \[
  \text{Perimeter} = (6x - 8) + (3x + 7) + (5x - 3)
  \]
  Simplifying:
  \[
  = 6x + 3x + 5x - 8 + 7 - 3
  = 14x - 4
  \]
  The perimeter of the blue triangle is \( 14x - 4 \).

---

Do you want more details on any of these solutions or have any questions?

### Relative Questions:
1. How would the perimeter change for the pink triangle if one side is doubled?
2. What happens to the perimeter of the yellow triangle if \( x \) equals 2?
3. Can the green triangle form a valid triangle for any \( x \)? Why or why not?
4. How would the perimeter of the blue triangle change if the constant terms were negative?
5. How does simplifying algebraic expressions affect finding the perimeter?

### Tip:
Always double-check your expression simplifications to ensure accuracy when calculating algebraic perimeters.

Can you find the perimeter of these triangles with algebraic expressions as side lengths?

Learn how to calculate the perimeter of triangles with side lengths expressed as algebraic expressions. This problem involves simplifying algebraic expressions to find the perimeters of four triangles. Suitable for students in Grades 7-9.

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