Question

Question : A square game board is divided into smaller squares, each with sides one-ninth the length of the sides of the board. Into how many squares is the game board divided?

Answer 1

Therefore the game board is divided into 81 smaller squares.

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
`\frac19x` units.

The area of a smaller square is
`=(\frac19x)* (\frac19x)`

`=(1)/(81)x^2`

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,

`a* ((1)/(81)x^2)=x^2`

`\Rightarrow a =(x^2* 81)/(x^2)`

`\Rightarrow a= 81`

Therefore the game board is divided into 81 smaller squares.