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प्रश्न
The area of a big rectangular room is 300 m2. If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.
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उत्तर
Let the original length and breadth of the rectangular room be x m and y m respectively.
Area of the rectangular room = xy = 300
`=> y = 300/x` ...(1)
New length = (x – 5) m
New breadth = (y + 5) m
New area = (x – 5)(y + 5) = 300 ...(Given)
Using (1), we have:
`(x - 5)(300/x + 5) = 300`
`300 + 5x - 1500/x - 25 = 300`
`5x - 1500/x - 25 = 0`
`5x^2 - 25x - 1500 = 0`
`x^2 - 5x - 300 = 0`
`x^2 - 20x + 15x - 300 = 0`
`x(x - 20) + 15(x - 20) = 0`
`(x - 20)(x + 15) = 0`
x = 20, –15
But, x cannot be negative.
So, x = 20.
Thus, the length of the room is 20 m.
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