Look at the patterns made by the matchsticks . Complete the tables and find a general formula.

Number of triangles (x) 1 2 3 4 5 6 7 8
Number of matchsticks (y) 3 6

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Solution

Number of matchsticks $(y) =$ $3 \times$ Number of triangles $(x)$
So, the general formula is
$y = 3 x$
Number of Triangles (x) 1 2 3 4 5 6 7 8
Number of matchsticks (y) 3 6 9 12 15 18 21 24

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Question 11(i)

Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

Look at the patterns made by matchsticks. Complete the tables and find a general formula.

Number of double squares (x)	1	2
Number of matchsticks (y)	7	12

(a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: if you remove the vertical stick at the end, you will get a pattern of Cs.)

(b) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

Q. Look at the following matchstick pattern of equilateral triangles.The triangles are not separate.Two neighbouring triangles have a common matchstick.Observe the pattern and find the rule that gives the number of matchsticks.

Q. Look at the following matchstick pattern of squares. The squares are not separate. Two neighboring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks.

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Number of Triangles (x)	1	2	3	4	5	6	7	8
Number of matchsticks (y)	3	6	9	12	15	18	21	24

Look at the patterns made by the matchsticks . Complete the tables and find a general formula. Number of triangles (x)12345678Number of matchsticks (y)36

Number of matchsticks (y)=3×Number of triangles(x)So, the general formula is y=3xNumber of Triangles (x)12345678Number of matchsticks (y)3691215182124

Look at the patterns made by the matchsticks . Complete the tables and find a general formula.

Number of triangles (x) 1 2 3 4 5 6 7 8
Number of matchsticks (y) 3 6

Number of matchsticks $(y) =$ $3 \times$ Number of triangles $(x)$
So, the general formula is
$y = 3 x$
Number of Triangles (x) 1 2 3 4 5 6 7 8
Number of matchsticks (y) 3 6 9 12 15 18 21 24