Question

a chessboard contains 64 equal squares and the area of each square is 625cm^2. A border around the board is 2 cm wide. find the length of a side and area of the chessboard.

( I will mark brainiest if correct with steps)

Answer 1

GIVEN

A chessboard contains 64 equal squares.

A chessboard contains 64 equal squares.

A chessboard contains 64 equal squares. The area of each square is 625cm^2.

A chessboard contains 64 equal squares. The area of each square is 625cm^2. A border around the board is 2 cm wide.

TO FIND :- Length and area of chess board.

SOLUTION :-

If area of each square is 625cmsq.

$area = {side}^{2} \\ \\ {625cm}^{2} = {side}^{2} \\ \\ \implies side = \sqrt{625} = 25cm$

Now, a chessboard is a square having

8 x 8 squares so...

Side of chessboard = 25 × 8 = 200cmsq.

But it has border of 2 cm( i.e. twice in one side)around it so length of side of the square becomes

200 + 2 + 2 = 204cm

Therefore area of the chessboard is :-

$area = {(side)}^{2} \\ \\ = 204 \times 204 \\ \\ = 41,616cmsq.$

Therefore, side of the board is 204cm and area is 41616cmsq.

Answer 2

Solution :-

Given : A chessboard contains 64 equal squares and the area of each square is 625 cm².

Area of 64 squares = (625 × 64) cm²

= 40000

Now,

Area of chessboard without the border :

Area of square = (side)²

=> 40000 = (side)²

=> √40000 = side = 200

Given : A border around the chessboard is 2 cm wide.

Length of chessboard including border = 200 + (2 × 2) = 204 cm

Area of chessboard including border :

Area of square = (side)²

= (204 cm)²

= 41616 cm²

Hence,

Length of chessboard including border = 204 cm

Area of chessboard including border = 41616 cm²