Question

problems 4 - 6: an equilateral triangle is a triangle where all three sides have the same length.

1. complete the table to show the side lengths and perimeters for several equilateral triangles.
2. explain why the relationship between the perimeter and side length for an equilateral triangle is proportional.
3. what is a constant of proportionality for the relationship?
4. these polygons are scaled copies. determine the perimeter of the larger polygon. show or explain your thinking.

Explanation:

Step1: Calculate perimeter for side length 3

Perimeter of equilateral triangle \(P = 3s\) (where \(s\) is side - length). For \(s = 3\), \(P=3\times3 = 9\).

Step2: Calculate perimeter for side length 10

Using \(P = 3s\), for \(s = 10\), \(P=3\times10=30\).

Step3: Calculate side length for perimeter 81

Since \(P = 3s\), then \(s=\frac{P}{3}\). For \(P = 81\), \(s=\frac{81}{3}=27\).

Step4: Calculate side length for perimeter 315

Using \(s=\frac{P}{3}\), for \(P = 315\), \(s=\frac{315}{3}=105\).

Answer:

Side Length	Perimeter
10	30
27	81
105	315