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.
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