The given figure gives a match stick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

(a) (b) (c) (d)

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Solution

From the figure, we observe that in the given matchstick pattern, the number of matchsticks are $3, 5, 7$ and $9$ which is $1$ more than the twice of the number of triangles in the pattern.
The number of matchsticks used in each pattern is $1$ more than $2$ times the number of triangles in it.
Therefore the pattern is $2 x + 1$ , where $x$ is the number of triangles.

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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.)

Find the rule which gives the number of matchsticks required to make the below matchstick pattern:-

A pattern of letter $R$ as $R$

Find the rule which gives the number of matchsticks required to make the below matchstick pattern:-

A pattern of the letter $A$ as A.

(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.

Question 11(ii)

Fig. below gives a matchstick pattern of triangles. As in Exercise 11(a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

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

The given figure gives a match stick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

(a) (b) (c) (d)