In a school, students were told to design a series of patterns with triangles and squares. Ian's group came up with the following series of patterns.
- How many squares did Ian's group need to form pattern 55?
- How many triangles did Ian's group need to form a pattern with 41 squares?
(a)
Patterns for the number of triangles and squares
Pattern 1: 1 triangle 5 squares
Pattern 2: 2 triangles 9 squares
Pattern 3: 3 triangles 13 squares
Formula:
Number of triangles = Pattern number
Pattern for the number of squares
Pattern 1: 1 + 1 x 4 = 5
Pattern 2: 1 + 2 x 4 = 9
Pattern 3: 1 + 3 x 4 = 13
Formula:
Number of squares = 1 + Pattern number x 4
Number of squares needed to form Pattern 55
= 1 + 55 x 4
= 221
(b)
1 + Pattern number x 4 = 41
Pattern number x 4 = 41 - 1 = 40
Pattern number = 40 ÷ 4 = 10
Pattern number = Number of triangles
Pattern number 10 = 10 triangles
Answer(s): (a) 221; (b) 10