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The graph shows the side lengths of equilateral triangles and their perimeters. What is the relationship between the triangle's side length and its perimeter?

The graph you uploaded shows the relationship between the side length of equilateral triangles (in inches) and their perimeters (in inches). Based on the pattern in the graph, it is clear that the perimeter increases linearly as the side length increases. 

For an equilateral triangle:
- The perimeter \( P \) is the sum of all three sides.
- If each side length is \( s \), the perimeter can be expressed as:

\[
P = 3 \times s
\]

Thus, the relationship between the side length \( s \) and the perimeter \( P \) is a direct proportion: 

\[
P = 3s
\]

This is confirmed by the graph, as each point indicates that as the side length increases by 1 inch, the perimeter increases by 3 inches.

Would you like further details or clarifications?

Here are 5 related questions:
1. How would the perimeter change if the side length doubled?
2. Can you calculate the perimeter of an equilateral triangle with a side length of 15 inches?
3. What is the slope of the line representing the perimeter as a function of the side length?
4. How does this relationship help in finding the side length if only the perimeter is known?
5. What would the graph look like if the triangles were isosceles instead of equilateral?

**Tip**: When dealing with geometric shapes, knowing one consistent property (like the side length in an equilateral triangle) helps easily derive others, such as the perimeter.

Explore how the perimeter of an equilateral triangle changes with its side length. This problem illustrates a direct proportionality between the side length and perimeter, with the perimeter formula P = 3s. Ideal for students in Grades 6-8.

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