Identify if this is a direct variation: The perimeter of p of a square whose side length is n

Yes, this is a **direct variation**.

The perimeter \( p \) of a square is given by the formula:

\[
p = 4n
\]

Where:
- \( p \) is the perimeter,
- \( n \) is the side length of the square.

In this equation, the perimeter \( p \) is directly proportional to the side length \( n \). This means that if you increase \( n \), \( p \) will increase in direct proportion, and vice versa. This fits the definition of a direct variation, which is represented as \( y = kx \), where \( k \) is a constant. Here, \( k = 4 \), the constant of proportionality.

Would you like more details or have any questions?

Here are five related questions:
1. What is the perimeter of a square if the side length \( n \) is 7 units?
2. How does the area of a square vary with the side length?
3. What is the difference between direct and inverse variation?
4. How can you identify the constant of proportionality in a direct variation problem?
5. How does the perimeter of a square compare to the perimeter of a rectangle?

**Tip:** Direct variation problems often involve a constant ratio between two variables, making them easy to spot when the equation has the form \( y = kx \).

Explore the concept of direct variation through the perimeter formula of a square. Understand how the perimeter p is directly proportional to the side length n with the formula p = 4n. Ideal for students in Grades 6-8 learning about geometry and proportional relationships.

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