Questions
In the diagram below the pattern with 1 triangle needs 3 rods. The pattern with 2 triangles needs 5 rods.
Try to answer the following questions using the diagram above.
Question
Complete the table for the number of rods needed for different numbers of triangles.
| Number of triangles (T) | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of rods (R) | 3 | 5 |
| Number of triangles (T) |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| Number of rods (R) |
|---|
| 3 |
| 5 |
The second row of the table should read 3, 5, 7, 9, 11, 13.
| Number of triangles (T) | 1 | 2 | 3 | 4 | 5 | 6 |
| Number of rods (R) | 3 | 5 | 7 | 9 | 11 | 13 |
| Number of triangles (T) |
|---|
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
| 6 |
| Number of rods (R) |
|---|
| 3 |
| 5 |
| 7 |
| 9 |
| 11 |
| 13 |
Question
Write down a formula for the number of rods, R, needed in a pattern with T triangles.
R is rising by 2 each time. This starts the formula with R = 2T, but in order for this formula to work for any number of triangles, we need to add 1.
So the formula is:
R = 2T + 1
Question
How many rods are needed for a pattern with 12 triangles?
R = 2T + 1
R = 2 x 12 + 1
R = 25
The number of rods needed is 25.
Question
How many triangles are there in a pattern using 49 rods?
In this question you already know the value of R. This time you need to work out R
R = 2T + 1
49 = 2T + 1
2T + 1 = 49
2T = 48
T = 24
The number of triangles in the pattern is 24.
