Answer:
Therefore the game board is divided into 81 smaller squares.
Step-by-step explanation:
Given that, there is a square game.
Consider x be length of one side the square.
The volume of the square is = side ×side
=x² square units
Since the length of side of smaller square is one-ninth of the game board.
Then one side length of the smaller square is [tex]\frac19x[/tex] units.
The area of a smaller square is [tex]=(\frac19x)\times (\frac19x)[/tex]
[tex]=\frac{1}{81}x^2[/tex]
Let a number of square is formed from the game board.
a ×The area of one smaller square= The area of game board.
According to the problem,
[tex]a\times (\frac{1}{81}x^2)=x^2[/tex]
[tex]\Rightarrow a =\frac{x^2\times 81}{x^2}[/tex]
[tex]\Rightarrow a= 81[/tex]
Therefore the game board is divided into 81 smaller squares.
