Study the pattern.
- Find the total number of white and grey triangles in Figure 100.
- Find the percentage of grey triangles in Figure 100.
(a)
Total number of triangles.
Figure 1: 1 = 1 x 1
Figure 2: 4 = 2 x 2
Figure 3: 9 = 3 x 3
Figure 4: 16 = 4 x 4
Figure 5: 25 = 5 x 5
Formula:
Total number of triangles = Figure number x figure number
Total number of grey and white triangles for Figure 100
= 100 x 100
= 10000
(b)
Difference in the number of white and grey triangles.
Figure 1: 1 - 0 = 1
Figure 2: 3 - 1 = 2
Figure 3: 6 - 3 = 3
Figure 4: 10 - 6 = 4
Formula:
Difference in the number of white and grey triangles = Figure number
Number of white triangles = 1 u
Number of grey triangles = 1 u + Figure Number
Total number of triangles
= 100 x 100
= 10000
1 u + 1 u + 100 = 10000
2 u = 10000 - 100
2 u = 9900
1 u = 9900 ÷ 2 = 4950
Number of grey triangles
= 1 u + 100
= 4950 + 100
= 5050
Percentage of grey triangles in Figure 100
=
505010000 x 100%
= 50.5%
Answer(s): (a) 10000; (b) 50.5%