To find the perimeter of each triangle, we will calculate the lengths of the sides based on the given expressions and add them.

Triangle 1:

Sides:

1. $3x$ (first side),
2. $6$ (second side),
3. $2(-2x + 16)$ (third side).

The perimeter of Triangle 1 is: $P_1 = 3x + 6 + 2(-2x + 16)$

Simplify the third side: $2(-2x + 16) = -4x + 32$

Substitute back into the perimeter equation: $P_1 = 3x + 6 - 4x + 32$

Combine like terms: $P_1 = -x + 38$

Triangle 2:

Sides:

1. $3x$ (first side),
2. $8$ (second side),
3. $2(5x - 14)$ (third side).

The perimeter of Triangle 2 is: $P_2 = 3x + 8 + 2(5x - 14)$

Simplify the third side: $2(5x - 14) = 10x - 28$

Substitute back into the perimeter equation: $P_2 = 3x + 8 + 10x - 28$

Combine like terms: $P_2 = 13x - 20$

Final Expressions:

• Perimeter of Triangle 1: $P_1 = -x + 38$
• Perimeter of Triangle 2: $P_2 = 13x - 20$

If you'd like, we can solve for $x$ or substitute a specific value to find numerical perimeters.

Do you want me to proceed with finding $x$ or calculate specific perimeters? Let me know!

Questions to Explore Further:

1. How can you determine $x$ for these triangles?
2. What happens to the perimeters if $x = 5$?
3. How would you interpret a negative perimeter result for $x$?
4. Are these triangles similar based on their side ratios?
5. Could the dimensions form valid triangles (Triangle Inequality Theorem)?

Tip: Always verify expressions and simplify carefully to avoid errors in geometric problems.