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
(b) Draw a graph using the first five pairs of numbers in your table.
(c) Do the points lie on a line?
Solution:
From the diagram above we can complete the table as shown:
| Side length of purpe tiles | 1 | 2 | 3 | 4 | 5 | 10 | 100 |
| Number of white tiles in border | 24 | 32 | 40 | 48 | 56 | 96 | 816 |
(b) The graph constructed using the first five pairs of numbers in the table above is shown below:
(c) As evident from above, the graph is a straight line.
✦ Try This: Regular polygons are shown below with their diagonals. Plot a graph between the number of sides of the polygon and the number of its diagonals and complete the table below
(a) Copy and complete the table
| Number of sides of Poygon | 4 | 5 | 6 | 7 | 8 | 9 |
| Number of diagonals |
(b) Draw a graph using the first three pairs of numbers in your table of the pairs and then using the graph complete the rest of the pairs of numbers.
(c) Do points lie on a straight line?
(a)The first three pairs of numbers are as follows:
| Number of sides of polygon | 4 | 5 | 6 |
| Number of diagonals | 2 | 5 | 9 |
The graph from the above given table we get:
(c) As evident from the above graph it is not a straight line. Hence points do not lie on a straight line and therefore it is not possible to calculate the number of diagonals of polygons of sides 7, 8 and 9 from the graph.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 15
NCERT Exemplar Class 8 Maths Chapter 12 Problem 85
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 (b) Draw a graph using the first five pairs of numbers in your table. (c) Do the points lie on a line?
Summary:
The graph is plotted between the side length of purple tiles and the number of white tiles in the border
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