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Given,
Area of rectangle = 25x
2 – 35x + 12
We know, area of rectangle = length × breadth
So, by factoring 25x
2 – 35x + 12, the length and breadth can be obtained. 25x
2 – 35x + 12 = 25x
2 – 15x – 20x + 12 => 25x
2 – 35x + 12 = 5x(5x – 3) – 4(5x – 3) => 25x
2 – 35x + 12 = (5x – 3)(5x – 4)
So, the length and breadth are (5x – 3)(5x – 4). Now, perimeter = 2(length + breadth)
So, perimeter of the rectangle = 2((5x – 3)+(5x – 4)) = 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14
So, the perimeter = 20x – 14.
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