Function P gives the perimeter of an equilateral triangle of side length "s".

It is represented by the equation P(s) = 3s.

Constructed Response Question
What is the independent variable (input)? What is the dependent variable (output)?
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In the function \( P(s) = 3s \), the independent variable (input) is the side length \( s \) of the equilateral triangle, as it can be chosen freely, and it determines the outcome of the function. The dependent variable (output) is the perimeter \( P \), as it depends on the value of \( s \).

In summary:
- **Independent variable (input)**: \( s \) (side length of the triangle)
- **Dependent variable (output)**: \( P \) (perimeter of the triangle)

Would you like additional explanations, or have questions on function variables? 

Here are some related questions to expand understanding:
1. What happens to the perimeter if we double the side length \( s \)?
2. How would you describe a dependent variable in other contexts?
3. If \( s = 5 \), what is the perimeter of the triangle?
4. Can the function \( P(s) = 3s \) apply to non-equilateral triangles?
5. How would you write a similar function for the area of an equilateral triangle?

**Tip:** Independent variables are often chosen freely, while dependent variables rely on the independent ones in equations.

What is the independent variable (input)? What is the dependent variable (output)?

Explore how to identify the independent and dependent variables in the perimeter function P(s) = 3s, where P is the perimeter of an equilateral triangle with side length s. Learn key geometry and function concepts, perfect for middle school students in Grades 6-8.

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