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

36 cm

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24 cm

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16 cm

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32 cm

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Solution

The correct option is
A

24 cm

Let the length of the side of the chess board be $x$ cm
Then, Area of 64 squares $= (x - 4)^{2}$
$∴ (x - 4)^{2} = 64 \times 6.25$
$\Rightarrow x^{2} - 8 x + 16 = 400$
$\Rightarrow x^{2} - 8 x - 384 = 0$
$\Rightarrow x^{2} - 24 x + 16 x - 384 = 0$
$\Rightarrow (x - 24) (x + 16) = 0 \Rightarrow x = 24 c m .$
(Neglect $x = - 16$ as length can not be negative.)

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A chess board contains 64 equal squares and the area of each square is 6.25 cm2. A border around the board is 2 cm wide. Find the length of the side of the chess board.

The correct option is A 24 cm Let the length of the side of the chess board be x cm Then, Area of 64 squares =(x−4)2 ∴(x−4)2=64×6.25 ⇒x2−8x+16=400 ⇒x2−8x−384=0 ⇒x2−24x+16x−384=0 ⇒(x−24)(x+16)=0⇒x=24 cm.(Neglect x=−16 as length can not be negative.)

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