A chess board contains 64 equal squares and the area of each square is `6. 25\ c m^2` . A border round the board is 2 cm wide. Find the length of the side of the chess board.

Answer

To find the length of the side of the chessboard, we can follow these steps:

### Step 1: Calculate the area of the chessboard
We know that the chessboard contains 64 equal squares and the area of each square is given as \(6.25 \, \text{cm}^2\).

\[ \text{Total Area} = \text{Area of one square} \times \text{Number of squares} = 6.25 \, \text{cm}^2 \times 64 \]

\[ \text{Total Area} = 400 \, \text{cm}^2 \]

### Step 2: Find the side length of the chessboard
Since the chessboard is square in shape, we can denote the length of one side of the chessboard as \(a\). The area of the chessboard can also be expressed as:

\[ a^2 = 400 \, \text{cm}^2 \]

To find \(a\), we take the square root of both sides:

\[ a = \sqrt{400} = 20 \, \text{cm} \]

### Step 3: Calculate the total length of the chessboard including the border
The problem states that there is a border of 2 cm wide around the chessboard. Therefore, the total length of the side of the chessboard including the border is:

\[ \text{Total Length} = \text{Border Width} + a + \text{Border Width} = 2 \, \text{cm} + 20 \, \text{cm} + 2 \, \text{cm} \]

\[ \text{Total Length} = 24 \, \text{cm} \]

### Final Answer
The length of the side of the chessboard is \(24 \, \text{cm}\).

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