The figure shows a pattern formed using some rods.
- How many rods are needed to form 16 triangles?
- How many triangles are formed using 57 rods?
1 triangle = 1 + (2 x 1) = 3 rods
2 triangles = 1 + (2 x 2) = 5 rods
3 triangles = 1 + (2 x 3) = 7 rods
Formula Number of rods = 1 + (2 x Number of triangles)
(a)
16 triangles
= 1 + 2 x 16
= 33 sticks
(b)
1 + (2 x Number of triangles) = 57 rods
2 x Number of triangles = 57 - 1 = 56 rods
Number of triangles = 56 ÷ 2 = 28
Answer(s): (a) 33; (b) 28