The area of a rectangular room is 45 meters square. If the length of the room is 3m less and breadth is 1m more, it will be a square room, find the length and the breadth of the room.

Let, length of the rectangular room (l) = x m

and breadth of the room (b) = y m

Here,

According to the first condition,

xy = 45 ..........(i)

Again, according to the second condition,

x - 3 = y + 1
x = y + 1 + 3
x = y + 4 ........(ii)

Putting the value of x from equation(ii) and equation (i), we get

(y + 4)y = 45
or, y² + 4y - 45 = 0
or, y² + (9-5)y - 45 = 0
or, y² + 9y - 5y - 45 = 0
or, y(y + 9) - 5(y + 9) = 0
or, (y + 9) (y - 5) = 0 

Either y + 9 = 0 ..........(iii)

Or, y - 5 = 0 ..........(iv)

From equation (iii)

y + 9 = 0
or, y = -9 which is impossible because length and breadth cannot be negative.

or, y = 5

Now, putting the value of y in equation (ii), we got,

x = 5 + 4

= 9

∴ Length of the room (l) = 9m and breadth of the room (b) = 5cm.