Triangles are made from matches of equal length.

Question

1 triangle=3 matches

2 triangles=12 matches

3 triangles=27matches

4 triangles= 48 matches

5 triangles = 75 matches

Using the values above, what is the rule linking the number of triangles(t), and the number of matches(m)?

Answer 1

a₁ = 3 = 3(1) = 3(1²)

a₂ = 12 = 3(4) = 3(2²)

a₃ = 27 = 3(9) = 3(3²)

a₄ = 48 = 3(16) = 3(4²)

a₅ = 75 = 3(25) = 3(5²)

 

Do you see the pattern?

 

a_n = 3n²  where n = number of triangles, a_n = number of matches used

 

m = 3t²  is the direct correlation