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The problem asks to write an expression in terms of \( n \) for the perimeter of the triangle.

### Perimeter of a Triangle:
The perimeter \( P \) of a triangle is the sum of all three side lengths. From the image, the three sides are:
- One side is labeled \( 7 \) (the base),
- Another side is labeled \( 5n \) (the slant height),
- The third side is labeled \( n \) (the vertical height).

Thus, the perimeter \( P \) is:
\[
P = 7 + 5n + n
\]

### Simplifying the Expression:
Combine like terms:
\[
P = 7 + 6n
\]

So, the expression for the perimeter in terms of \( n \) is:
\[
P = 6n + 7
\]

Would you like further clarification or details on this solution? Here are some related questions you might find useful:

1. How would the perimeter change if one side were doubled?
2. Can we apply this perimeter formula to any triangle? Why or why not?
3. What is the relationship between the side lengths of a right triangle?
4. How can we use the Pythagorean theorem to solve for unknown side lengths in a right triangle?
5. How would you find the area of this triangle if it were given as a right triangle?

**Tip**: When simplifying expressions, always combine like terms to make calculations more straightforward.

Write an expression in terms of n for the perimeter of this triangle. Simplify your answer.

Learn how to write an expression for the perimeter of a triangle in terms of n. This problem involves calculating the perimeter using linear expressions and simplifying the result. Suitable for students in Grades 7-9.

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