The figure shows a pattern formed using some sticks.
- How many sticks are needed to form 28 triangles?
- How many triangles are formed using 105 sticks?
Pattern for the total number of triangles
1 triangle: 1 + (2 x 1) = 3 sticks
2 triangles: 1 + (2 x 2) = 5 sticks
3 triangles: 1 + (2 x 3) = 7 sticks
Formula
Number of sticks = 1 + (2 x Number of triangles)
(a)
28 triangles: 1 + 2 x 28 = 57 sticks
(b)
1 + (2 x Number of triangles) = 105
2 x Number of triangles = 105 - 1
2 x Number of triangles = 104
Number of triangles = 104 ÷ 2 = 52
Answer(s): (a) 57; (b) 52
