Question

A chess board contains $64$ equal squares and the area of each square is $6.25{\text{cm}}^2$. A border round the board is $2\text{cm}$ wide. Find the length of the side of the chess board.

Answer 1

Let the length of the side of the chess board be $x\text{cm}$.

Then, Area of $64$ squares $={(x-4)}^2$

${(x-4)}^2=64\times 6.25$

$x^2-8x+16=400$

$x^2-8x-384=0$

Splitting the middle term:

$x^2-24x+16x-384=0$

$(x-24)(x+16)=0$

$x=24\text{cm}$