Question

A chessboard contains 64 equal squares and the area of each square is $6.25c{m}^2$. A border around the board is 2 cm wide. Find the length of the side of the chess board.

Answer 1

Let the length of the side of the chessboard be x cm.
Then, Area of 64 squares $=(x-4{)}^2$
$\therefore (x-4{)}^2=64\times 6.25\Rightarrow x^2-8x+16=400\Rightarrow x^2-8x-384=0\Rightarrow x^2-24x+16x-384=0\Rightarrow (x-24\left)\right(x+16)=0\Rightarrow x=24cm.or-16$

The length cannot be negative.

Length of the chess board is 24 cm.