A triangle pattern is shown below.
Three images are shown of a triangle patternThe first image shows one isosceles triangle. The base is labeled 6 and the other two sides are labeled 9. The second image shows two adjacent isosceles triangles. The original triangle is there, and now another upside down triangle is adjacent to it. Both triangles are the same size, with bases labeled 6 and the other two sides labeled 9. The third image shows three adjacent isosceles triangles. The two triangles from the second image are there, and now another right side up triangle is adjacent to the upside down one. All three triangles are the same size, with bases labeled 6 and the other two sides labeled 9.
The perimeter of each figure in the pattern is shown in the table below.
Figure Perimeter
1 triangle 24
2 triangles 30
3 triangles 36
Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (P)?
(1 point)
Responses
P = 6n + 18
P = 6 n + 18
P = 9n + 6
P = 9 n + 6
P = 6n + 9
P = 6 n + 9
P = 9n + 12
P = 9 n + 12
The correct equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P) is:
P = 9n + 6
The correct equation relating the number of triangles in the figure (n) to the perimeter of the figure (P) is:
P = 9n + 6
To determine the correct equation relating the number of triangles (n) to the perimeter (P) of the figure, let's analyze the pattern provided.
Given that the base of each triangle is labeled 6 and the other two sides are labeled 9, we can observe that the perimeter of each triangle is the sum of its three sides, which are 6, 9, and 9.
In the first figure, which consists of a single triangle, the perimeter is given as 24. Thus, we can deduce that:
Perimeter of 1 triangle = 6 + 9 + 9 = 24
In the second figure, which consists of two adjacent triangles, the perimeter is given as 30. Since both triangles have the same size and their bases are adjacent, we can calculate the perimeter as follows:
Perimeter of 1 triangle + Perimeter of 1 triangle = 30
(6 + 9 + 9) + (6 + 9 + 9) = 30
30 = 30
In the third figure, which contains three adjacent triangles, the perimeter is given as 36. Again, we can calculate the perimeter of three triangles:
Perimeter of 1 triangle + Perimeter of 1 triangle + Perimeter of 1 triangle = 36
(6 + 9 + 9) + (6 + 9 + 9) + (6 + 9 + 9) = 36
36 = 36
By analyzing the pattern, we can conclude that the perimeter (P) is related to the number of triangles (n) in the figure by the equation:
P = 6n + 18
Hence, the correct equation for relating the number of triangles (n) to the perimeter (P) of the figure is:
P = 6n + 18