Answer

Verified

417k+ views

**Hint:**Assume that there are ‘n’ squares along each side of the chess game board. Consider ‘x’ as the length of each small square. Now, use the area relation that ‘area of these 64 small squares will be equal to the square of n times the length of each small square along each side’. Cancel the common factors and find the value of ‘n’.

**Complete step-by-step solution:**

Here, we have been provided with the information that a chessboard has 32 black and 32 white squares. We are asked to determine the number of squares along each side of the chess board.

Let us assume that there are ‘n’ small squares along each side of the chessboard and the length of each side of these small squares is ‘x’. So, we have,

\[\because \] Total number of squares = Number of (black squares + white squares)

\[\Rightarrow \] Total number of squares = 32 + 32 = 64

So, there are 64 small squares in a chess board, therefore the area of these 64 small squares must be equal to \[nx\times nx\], because each side contains n small squares and the length of each side of these squares is x. So, we have on equating the areas,

\[\begin{align}

& \Rightarrow nx\times nx=64\times {{x}^{2}} \\

& \Rightarrow {{n}^{2}}{{x}^{2}}=64{{x}^{2}} \\

\end{align}\]

Cancelling the common factor from both the sides, we get,

\[\Rightarrow {{n}^{2}}=64\]

Taking square root on both the sides, we have,

\[\begin{align}

& \Rightarrow n=\sqrt{64} \\

& \Rightarrow n=8 \\

\end{align}\]

**Hence, there are 8 small squares along each side of the chess board.**

**Note:**One may check the answer by considering 8 columns and 8 rows in the game board and adding eight times. Remember that there are alternate black and white squares in the game board. In the above question there was no need of assuming the length of each side of the small square as x, we can directly get the answer by taking under root of the number 64 because in the end the variable x is getting cancelled.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

A rainbow has circular shape because A The earth is class 11 physics CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell