A chessboard contain 64 equal squarres and the area of each square is 6.25 sq. cm if there is a border round it of 1.5 cm width then line length of the side of the chessboard is

Options

A. 23 cm
B. 21 cm
C. 19 cm
D. 17 cm

Answer

To find the length of the side of the chessboard with a border, we will follow these steps:

### Step 1: Calculate the area of the chessboard
Since the chessboard contains 64 equal squares, and the area of each square is given as 6.25 cm², we can calculate the total area of the chessboard.

\[ \text{Total Area} = \text{Number of Squares} \times \text{Area of Each Square} \]
\[ \text{Total Area} = 64 \times 6.25 = 400 \text{ cm}^2 \]

### Step 2: Find the side length of the chessboard
The area of a square is given by the formula \( \text{Area} = \text{side}^2 \). To find the side length of the chessboard, we take the square root of the total area.

\[ \text{Side Length} = \sqrt{\text{Total Area}} = \sqrt{400} = 20 \text{ cm} \]

### Step 3: Account for the border
The border around the chessboard has a width of 1.5 cm on each side. Therefore, we need to add twice the width of the border to the side length of the chessboard.

\[ \text{Total Length with Border} = \text{Side Length} + 2 \times \text{Border Width} \]
\[ \text{Total Length with Border} = 20 \text{ cm} + 2 \times 1.5 \text{ cm} = 20 \text{ cm} + 3 \text{ cm} = 23 \text{ cm} \]

### Final Answer
The length of the side of the chessboard, including the border, is **23 cm**.

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