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.

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Solution

Figure
Number of triangles
Number of matchsticks Pattern
$(i)$ $1$ $3$ $2 \times 1 + 1$
$(i i)$ $2$ $5$ $2 \times 2 + 1$
$(i i i)$ $3$ $7$ $2 \times 3 + 1$
Number of matchsticks required $= 2 x + 1$ , 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.)

Question 11(i)

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)

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Figure	Number of triangles	Number of matchsticks	Pattern
$(i)$	$1$	$3$	$2 \times 1 + 1$
$(i i)$	$2$	$5$	$2 \times 2 + 1$
$(i i i)$	$3$	$7$	$2 \times 3 + 1$

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.

Figure Number of triangles Number of matchsticks Pattern(i) 1 3 2×1+1(ii) 2 5 2×2+1(iii) 3 7 2×3+1Number of matchsticks required =2x+1, where x is the number of triangles

Figure
Number of triangles
Number of matchsticks Pattern
$(i)$ $1$ $3$ $2 \times 1 + 1$
$(i i)$ $2$ $5$ $2 \times 2 + 1$
$(i i i)$ $3$ $7$ $2 \times 3 + 1$
Number of matchsticks required $= 2 x + 1$ , where $x$ is the number of triangles