In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.
Hint : Create equations on the basis of given conditions.
Let the length of the rectangle be $x$ metres and the breadth be $y$ metres. Area of the rectangle $ = length \times breadth = x \times y = xy$ sq. metres From the given information, we have, \[(x + 3) \times (y - 4) = xy - 67\] & \[(x - 1) \times (y + 4) = xy + 89 \\\]