Question

A square chessboard has 32 black and 32 white squares each of area 6.25 cm². A border around a chessboard is of width 3 cm. find the length of one side of chessboard. ($\mathrm{\pi }=3.14$).

Answer 1

Number of black squares = 32
Number of white squares = 32
Total number of squares = 32 + 32 = 64
Area of 1 square = 6.25 cm²
Area of 64 square = 6.25 × 64 cm² = 400 cm²
$\therefore$ Area of the chessboard excluding the border = 400 cm²
Let the side of the chessboard excluding the border be s cm.
$\therefore$ (s)² = 400
$\Rightarrow$ s = 20 cm
i.e., side of the chessboard excluding the border = 20 cm
$\therefore$ Side of the chessboard including the border = 20 + 3 + 3 cm = 26 cm