A triangle pattern is shown below. The 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)?
The equation that relates the number of triangles (n) to the perimeter of the figure (P) can be determined by examining the given perimeters in the table.
From the table, we can observe that as the number of triangles increases, the perimeter also increases.
By comparing the number of triangles (n) to the corresponding perimeter (P) in the table, we can see that the perimeter of each figure can be calculated by multiplying the number of triangles by a constant value of 6.
Therefore, the equation that relates the number of triangles (n) to the perimeter of the figure (P) is:
P = 6n
The equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P) is:
P = 24 + 6n
To determine the equation that relates the number of triangles in the figure (n) to the perimeter of the figure (P), we need to analyze the given information.
From the pattern outlined, we can observe that when we add one more triangle to the figure, the perimeter increases by 6 units.
Let's break it down:
- For the first image with one triangle, the perimeter is 24.
- For the second image with two triangles, the perimeter is 30. The increase in perimeter from the first image to the second image is 30 - 24 = 6 units.
- For the third image with three triangles, the perimeter is 36. The increase in perimeter from the second image to the third image is 36 - 30 = 6 units.
We can see that for each additional triangle added to the figure, the perimeter increases by 6 units consistently.
Therefore, we can conclude that the equation relating the number of triangles (n) to the perimeter (P) is:
P = 24 + 6n
In this equation, 24 represents the initial perimeter of one triangle, and 6n represents the increase in perimeter for each additional triangle.
So, if you know the number of triangles (n), you can use this equation to calculate the corresponding perimeter (P).