question_answer 1)

(i) Look at the following matchstick pattern of squares. The squares are not separate. Two neighboring 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.) (ii) Figure depict 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.                

Answer:

                (i) In figures, Number of squares = 1 and number of matchsticks \[=4=3\times 1+1\] = 3 \[\times \] Number of square + 1 (b) Number of squares = 2 and number of matchsticks \[=7=3\times 2+1\] = 3 \[\times \] Number of squares + 1 (c) Number of squares = 3 and number of matchsticks \[=10=3\times 3+1\] = 3 \[\times \] Number of squares + 1 (d) Number of squares = 4 and number of matchsticks \[=13=3\times 4+1\] = 3 \[\times \] Number of squares + 1 Thus, if number of squares \[=x\] Then, number of matchsticks \[=3\times \] Number of squares + 1  \[=3x+1\] Hence, the required rule that gives the number of matchsticks is \[3x+1,\] where \[x\] is number of squares. (ii) In figures,                                                              Number of triangles = 1 and number of matchsticks \[=3=2\times 1+1\] = 2\[\times \]Number of triangle + 1 (b) Number of triangles = 2 and number of matchsticks \[=5=2\times 2+1\] = 2\[\times \]Number of triangles + 1 (c) Number of triangles = 3 and number of matchsticks \[=7=2\times 3+1\] = 2\[\times \]Number of triangles + 1 (d) Number of triangles = 4 and number of matchsticks \[=9=2\times 4+1\] = 2\[\times \]Number of triangles + 1 Thus, if number of triangles \[=x\] Then, number of matchsticks \[=2\times \] Number of triangles \[+1=2x+1\] Hence, the required rule that gives the number of matchsticks is \[2x+1,\] where \[x\] is number of triangles.