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To solve for the perimeter of the triangle, you need to add up all the side expressions.

The side lengths given are:

- \( 8x - 7w \)
- \( 4x + 9y \)
- \( 3y + 4w \)

The perimeter \( P \) of the triangle is simply the sum of these expressions:

\[
P = (8x - 7w) + (4x + 9y) + (3y + 4w)
\]

Now, let's combine the like terms:

- For \( x \): \( 8x + 4x = 12x \)
- For \( w \): \( -7w + 4w = -3w \)
- For \( y \): \( 9y + 3y = 12y \)

Thus, the simplified expression for the perimeter is:

\[
P = 12x - 3w + 12y
\]

Would you like further clarification or details on any step?

Here are some related questions you might explore:
1. How do you find the perimeter of a shape with variable expressions?
2. What are the steps to combine like terms in algebraic expressions?
3. How would the perimeter change if one of the side lengths was a constant instead of a variable expression?
4. What is the difference between factoring and simplifying expressions?
5. Can you find the perimeter of other polygons with variable expressions?

**Tip:** Always group like terms (terms with the same variable) when simplifying algebraic expressions.

Write down a simplified expression for the perimeter of this triangle with side lengths: 8x - 7w, 4x + 9y, 3y + 4w.

Find the simplified expression for the perimeter of a triangle with sides: 8x - 7w, 4x + 9y, and 3y + 4w. This solution explains how to combine like terms and simplify variable expressions. Suitable for students in Grades 7-9.

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