https://file.aiquickdraw.com/mathbot/file/1726756566053irhwscnv.jpg

The image shows a triangle with sides labeled as expressions in terms of \( y \). The sides of the triangle are:

- \( 3y + 5 \)
- \( 6y \)
- \( y - 4 \)

To find the perimeter of the triangle, we simply add these expressions together:

\[
\text{Perimeter} = (3y + 5) + 6y + (y - 4)
\]

Now, let's simplify this expression by combining like terms:

\[
\text{Perimeter} = 3y + 6y + y + 5 - 4
\]

\[
\text{Perimeter} = (3y + 6y + y) + (5 - 4)
\]

\[
\text{Perimeter} = 10y + 1
\]

Thus, the perimeter of the triangle as a simplified expression is:

\[
\boxed{10y + 1}
\]

Would you like further details or explanations?

Here are five related questions to expand your understanding:
1. How would the perimeter change if one side were doubled?
2. How do you find the perimeter of a triangle if the sides are given as fractions?
3. Can you write the expression for the area of this triangle using Heron's formula?
4. What would the perimeter be if \( y = 2 \)?
5. How do you find the perimeter of a triangle with sides that contain square roots?

**Tip:** Always combine like terms when simplifying algebraic expressions to avoid mistakes.

Write the perimeter of the triangle as a simplified expression.

Learn how to calculate the perimeter of a triangle with sides expressed as algebraic terms. This problem covers simplifying expressions and adding like terms to find the perimeter. Suitable for students in Grades 7-9.

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