**The equilateral triangles below are formed using 2 cm sticks.**

**a) How many sticks are needed to form Pattern 5?**

b) In which pattern will each side of the triangle measure 30 cm?

c) Calculate the number of shaded triangles in Pattern 100.

Solution

b) In which pattern will each side of the triangle measure 30 cm?

c) Calculate the number of shaded triangles in Pattern 100.

Solution

**b)**

Pattern 1 --> 1 x 2cm = 2 cm

Pattern 2 --> 2 x 2cm = 4 cm

Pattern 3 --> 3 x 2cm = 6 cm

:

:

:

Pattern 15 --> 15 x 2cm = 30 cm

**Answer: Pattern 15**

From above

1 + 2 + 3 ..... + 100

1 + 99 = 100

2 + 98 = 100

3 + 97 = 100

:

:

49 + 51 = 100

(only 50 is not paired)

49 groups of 100 --> 4900

Add the unpaired 50 --> 4900 + 50 = 4950

**Answer: 4950 shaded triangles**

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