#### 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.

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.