A chess board contains 64 equal squares and the area of each square is

1.	A chess board contains 64 equal squares and the area of each square is 6.25 cm2A border around the board is 2cm wide. Find the length of the side of the chess board.
Answer» Let the length of the side of a chessboard be x cm. Area of 1 square in chessboard= 6.25 cm² area of 64 squares= 64 × 6.25 Area of 64 square = (x - 4)² 64 × 6.25 = (x - 4)²400 = (x - 4)²400 = x² + 4² -2×x×4[(a-b)²= a²+b² -2ab] 400 = x² +16 -8x400 -16 = x²+16384 = x²+16x² +16 -384 = 0x² -24x +16x -384= 0x(x -24) + 16 ( x - 24) = 0(x -24) (x +16) = 0 (x -24) = 0 or (x +16) = 0 x = 24 or x= -16 Length can't be negative, so x= 24. Hence the Length of the side of the chess board= 24 cm.

A chess board contains 64 equal squares and the area of each square is 6.25 cm2A border around the board is 2cm wide. Find the length of the side of the chess board.

Answer»

Let the length of the side of a chessboard be x cm.

Area of 1 square in chessboard= 6.25 cm²

area of 64 squares= 64 × 6.25

Area of 64 square = (x - 4)²

64 × 6.25 = (x - 4)²400 = (x - 4)²400 = x² + 4² -2×x×4[(a-b)²= a²+b² -2ab]

400 = x² +16 -8x400 -16 = x²+16384 = x²+16x² +16 -384 = 0x² -24x +16x -384= 0x(x -24) + 16 ( x - 24) = 0(x -24) (x +16) = 0

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

x = 24 or x= -16

Length can't be negative, so x= 24.

Hence the Length of the side of the chess board= 24 cm.