A rectangle has an area of 36 cm and perimeter of 30cm Find the larger side of it.
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Let Larger( length ) side be ( x cm ) and Shorter side be ( 36 / x )
Given, Perimeter = 30
2( length + breadth ) = 30
=> x + ( 36 / x ) = 15
=> ( x^2 + 36 ) / x = 15
=> x^2 + 36 = 15x
=> x^2 - 15x + 36 = 0
=> x^2 - ( 12 + 3 ) x + 36 = 0
=> x^2 - 12x - 3x + 36 = 0
=> x( x - 12 ) - 3( x - 12 ) = 0
=> ( x - 12 ) ( x - 3 ) = 0
=> x - 12 = 0 Or x - 3 = 0
=> x = 12 Or x = 3
Hence, x = 12 cm [ Taking larger one ]
Larger side = x = 12 cm
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