Question

Sonal and Anmol made a sequence of tile designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.

(a) Copy and complete the table

Side Length of Purple Titles	1	2	3	4	5	10	100
Number of white Tiles in Border

(b) Draw a graph using the first five pairs of numbers in your table.

(c) Do the points lie on a line?

Answer 1

(a) In side length 1 the number of white tile surrounding purple tile is 4.

Similarly, in side length 2 the number of white tiles surrounding purple tile is 8.

Thus, we can arrange the following table which shows side length of purple corresponding to the number of white tiles in border.

Side length of purple	1	2	3	4	5	10	100
Number of while titles in border	4	8	12	16	20	40	400

Hence, the table shows y = 8x + 16.

(b) On the basis of tables given in sol. (a) part, we draw the following graph

(c) If we join all points in above graph, we get a straight line. This shows, that all points lies on a line.