Question

Question 85(i)
Sonal and Anmol made a sequence of the designs from square white tiles surrounding one square purple tile. The purple tiles come in many sizes. Three of the designs are shown below.

Copy and complete the table
$\begin{array}{ccccccc}Sidelengthofpurple& 1& 2& 4& 5& 10& 100\\ Numberofwhitetilesinborder& & & & & & \end{array}$

Answer 1

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.
$\begin{array}{cccccccc}Sidelengthofpurple& 1& 2& 3& 4& 5& 10& 100\\ Numberofwhitetilesinborder& 4& 8& 12& 16& 20& 40& 400\end{array}$
Hence, the table shows $y=4x$.