Jeff made some designs using equilateral triangles, as shown bellow. He noticed that as he added new triangles, there was a relationship between the number of triangles, and the outer perimeter of the design.
If the pattern is continued, what would be the outer perimeter of a design using 7 triangles?
(Assume the length of a side of a triangle to be 1)
To determine the outer perimeter of a design using 7 triangles, we first need to understand the pattern between the number of triangles and the outer perimeter.
Let's analyze the given designs made by Jeff:
- Design with 1 triangle: In this case, the outer perimeter is simply the perimeter of the single triangle, which has three sides with a length of 1. So, the outer perimeter is 3.
- Design with 2 triangles: To form a design with 2 triangles, we need to connect the two triangles at their common side. This results in two sides that are shared by the triangles, each with a length of 1, and one additional side formed by the connection, also with a length of 1. So, the outer perimeter is 1 + 1 + 1 = 3.
- Design with 3 triangles: Similarly, to form a design with 3 triangles, we connect them in a way that shares their sides. This results in three shared sides, each with a length of 1, and three additional sides formed by the connections, also with a length of 1. So, the outer perimeter is 1 + 1 + 1 + 1 + 1 + 1 = 6.
From the analysis above, we can observe that the outer perimeter of the design is equal to the number of triangles being used.
Therefore, for a design using 7 triangles, the outer perimeter would be 7.
So, the outer perimeter of a design using 7 triangles would be 7.