To find the perimeter of the triangle, we need to sum the lengths of its three sides.

The side lengths are given as:

• $(6v + 3)$ cm
• $(2v + 5)$ cm
• $(8w + 5)$ cm

The perimeter $P$ of the triangle is the sum of these three expressions:

$P = (6v + 3) + (2v + 5) + (8w + 5)$

Now, combine like terms:

• For the terms involving $v$, we have $6v + 2v = 8v$.
• For the constant terms, we have $3 + 5 + 5 = 13$.
• The term with $w$ remains as $8w$.

So, the expression for the perimeter is:

$P = 8v + 8w + 13 \ \text{cm}$

This is the expression that represents the perimeter of the triangle.

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Would you like further details or clarification? Here are a few related questions you may find useful:

1. How do you calculate the perimeter of a triangle if the side lengths are expressed as algebraic expressions?
2. What is the process for simplifying algebraic expressions when adding them together?
3. How can you solve for the value of $v$ or $w$ if additional information about the perimeter is provided?
4. What are some real-world applications of finding the perimeter of a triangle using algebraic expressions?
5. Can a triangle's perimeter ever be negative? What would that imply?

Tip: Always combine like terms when simplifying algebraic expressions. This makes the problem easier to handle and helps avoid mistakes.