Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Last updated at May 29, 2023 by Teachoo

Ex 11.1, 11 (a) Look at the following matchstick pattern of squares (Fig 11.6). 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.) We notice that, If we remove one matchstick from the end We get a pattern of Cs We notice that, If we remove one matchstick from the end We get a pattern of Cs And, Number of C’s = 3n So, if we add 1 vertical line to pattern of C’s We get our squares So, Number of matchsticks = 3 × Number of squares + 1 Writing x = Number of squares Number of matchsticks = 3x + 1 where x is the Number of squares Ex 11.1, 11 (b) Fig 11.7 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. . We see that, 1st triangle requires 3 matchsticks 2nd triangle requires 3 matchsticks of 1st triangle & 2 new matchsticks 3rd triangle requires 3 matchsticks of 1st triangle & 2 new matchsticks of 2nd triangle & 2 new matchsticks of So, every new triangle requires 2 matchsticks for each triangle & 1 additional matchstick So, Number of matchsticks = 2 × number of triangles + 1 Writing x = Number of triangles Number of matchsticks = 2𝑥 + 1 where x is number of triangle.