Question

A chess board contains 64 equal squares and the area of each square is 6.25 cm${}^2$. A border round 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 chess board be $x$ cm. Then,

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

Therefore,

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

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

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

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

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

$x=24$ $cm$