Question

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Answer 1

Let the length of the rectangle be x units and the breadth of the rectangle be y units.
We know that, area of a rectangle = length x breadth = xy
According to the question,
xy - 9 = ( x - 5 )( y + 3 )
⇒ xy - 9 = xy + 3x - 5y - 15
⇒  3x - 5y = 6                         ....(1)

xy + 67 = ( x + 3 )( y + 2 )
⇒ xy + 67 = xy + 2x + 3y + 6
⇒  2x + 3y = 61                      ...(2)

Multiply (1) by 2 and (2) by 3, we get
6x - 10y = 12                           ...(3)
6x + 9y = 183                          ...(4)

Subtracting equation (4) from (3),
    6x - 10y = 12
-   6x + 9y = 183
    -    -         -      
         - 19y = - 171
               y = 9
Putting y = 9 in equation (1)
3x - 5y = 6
3x - 5(9) = 6
3x = 6 + 45
x = `51/3`
x = 17
Hence, the length of the rectangle is 17 units and the breadth of the rectangle is 9 units.