length of a rectangle is 5 cm more than twice of its breadth if area of the rectangle is 1950 square cm then find the perimeter of rectangle
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Let the breadth of the rectangle be 'x' and that of length be 'y'.
According to the given condition,
→ y = 2x + 5
Also it is given that the area of the rectangle is 1950 cm².
→ Area of rectangle = length × breadth
→ Area = ( 2x + 5 ) ( x ) = 1950 cm²
→ 2x² + 5x = 1950
→ 2x² + 5x - 1950 = 0
→ 2x² + 65x - 60x - 1950 = 0
→ x ( 2x + 65 ) - 30 ( 2x + 65 ) = 0
→ ( x - 30 ) ( 2x + 65 ) = 0
→ x = -32.5, 30
Hence the breadth of the rectangle is 30 cm as length cannot be negative.
Therefore length is equal to:
→ 2 ( 30 ) + 5
→ 60 + 5
→ 65 cm
Therefore Perimeter of a rectangle = 2 ( l + b )
→ 2 ( 30 + 65 )
→ 2 ( 95 )
→ 190 cm
Therefore the perimeter of the rectangle is 190 cm.
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