(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 below figure gives a matchstick pattern of triangles. As in Exercise 11 (a) above

To do:

We have to find the general rule that gives the number of matchsticks in each case.

Solution:

(a) We can observe that,

In the given pattern, the number of matchsticks are 4, 7, 10, 13,......

$4=3\times1+1$

$7=3\times2+1$

$10=3\times3+1$

$13=3\times4+1$

Therefore, the number of matchsticks $=3\times$ number of squares in the pattern $+1$

The required pattern is $3x + 1$, where $x$ is the number of squares.

(b) We can observe that,

In the given pattern, the number of matchsticks are 3, 5, 7, 9,......

$3=2\times1+1$

$5=2\times2+1$

$7=2\times3+1$

$9=2\times4+1$

Therefore, the number of matchsticks $=2\times$ number of triangles in the pattern $+1$

The required pattern is $2x + 1$, where $x$ is the number of triangles.

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Updated on: 10-Oct-2022

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