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# 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. - Mathematics

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#### Question

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.

#### Solution

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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