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Let width of rectangle w = x cm

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Length is 4 cm longer than it is wide

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Length of rectangle l = (x+4) cm

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Diagonal of rectangle d = 20 cm

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Length , width , Diagonal are forms right angled triangle.

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Length² + width² = Diagonal²

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(x+4)² + x² = 20²

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x² + 8x + 16 + x² = 400

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2x² + 8x + 16 - 400 = 0

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2x² + 8x - 384 = 0

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x² + 4x - 192 = 0

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For factoring above equation, appropriate factor is 192 = 12×16

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x²  + 16x - 12x - 192 = 0

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x ( x + 16 ) - 12 ( x  + 16 ) = 0

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( x + 16 ) ( x - 12 ) = 0

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By using zero product property : If AB = 0 then A = 0 , B = 0

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( x + 16 ) = 0  and  ( x - 12 ) = 0

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( x + 16 ) = 0 then x = -16 is invalid.Since negative dimensions are not exists.

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( x - 12 ) = 0 then  x = 12 cm is valid

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Width of rectangle w = 12 cm

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Length of rectangle l = (12+4) = 16 cm

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Final Answer :

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The dimensions of the rectangle :  Width is 12 cm , Length is 16 cm

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