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

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 $\frac19x$ units.

The area of a smaller square is $=(\frac19x)\times (\frac19x)$

                                                    $=\frac{1}{81}x^2$

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,

$a\times (\frac{1}{81}x^2)=x^2$

$\Rightarrow a =\frac{x^2\times 81}{x^2}$

$\Rightarrow a= 81$

Therefore the game board is divided into 81 smaller squares.