Question

A chess board contains 64 equal squares and the area of each square is 6.25cm². 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 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)²
400 = (x - 4)²
400 = x² + 4² -2×x×4
[(a-b)²= a²+b² -2ab]

400 = x² +16 -8x
400 -16 = x²+16
384 = x²+16
x² +16 -384 = 0
x² -24x +16x -384= 0
x(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.

HOPE THIS WILL HELP YOU...

Answer 2

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Nice Questions! ♥

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Ans:

Let x be the side length of the square board

Area of one square in the chess board = 6.25 cm²

Area of 64 squares = 64 x 62.5

                   (x – 4)² = 400                                     

                   (x – 4)  = √400

                     (x – 4)  = √20 x 20

                      x – 4 = 20

                          x = 20 + 4

                          x = 24 cm                                 

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