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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Solution

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

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

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.

Question 1(iv)

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule
A pattern of letter V as

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Writing Patterns in Geometry

Standard VI Mathematics

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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.

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 = 2x+1.

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.