Each of the figures is made up of 1-cm toothpicks.
The table shows the number of toothpicks used to make the figures and their perimeters.

1. Find the number of toothpicks in Figure 8.
2. What is the perimeter of Figure 58?
3. Which figure requires a total number of 1975 toothpicks?

(a)
Pattern for the number of toothpicks
Figure 1: 1 x 8 + 7 = 15
Figure 2: 2 x 8 + 7 = 23
Figure 3: 3 x 8 + 7 = 31

Formula:
Number of toothpicks = Pattern number x 8 + 7

Number of toothpicks in Figure 8
= 8 x 8 + 7
= 71

(b)
Pattern for the perimeter of the figure
Figure 1 = 1 x 2 + 7 = 9
Figure 2 = 2 x 2 + 7 = 11
Figure 3 = 3 x 2 + 7 = 13

Formula:
Perimeter of the figure = Pattern number x 2 + 7

Perimeter of figure 58
= 58 x 2 + 7
= 123

(c)
Figure number x 8 + 7 = 1975
Figure number x 8 = 1975 - 7 = 1968
Figure number = 1968 ÷ 8 = 246

Answer(s): (a) 71; (b) 123; (c) 246