What is the rule that gives the number of matchsticks in terms of the number of triangles, as shown in the figures below?

4 x + 1

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3 x + 1

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2 x + 1

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2 x

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Solution

The correct option is C $2 x + 1$

The column of 'number of matchsticks - 1' forms the multiplication table of 2, i.e., 2, 4, 6, 8, ...

Let the number of triangles be $x$ .

The number of matchsticks used in each pattern is 1 more than 2 times the number of triangles in it.

$∴$ The number of matchsticks used in each pattern = $2 x + 1$

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Similar questions

Q. What is the general rule that gives the number of matchsticks in terms of the number of triangles as shown in the figure?

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.

(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 squares. The squares are not separate. Two neighbouring squares have a common matchstick. What is the rule that gives the number of matchsticks in terms of the number of squares?
(Let the number of squares be x)

Q. What is the rule for the number of matchsticks for the pattern below if 'n' represents the number of squares ?

( 4 line segments in 1 square are considered as 4 matchsticks )

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