The area of a rectangle gets reduced by 67 square metres, when its length is increased by 3 m and breadth is decreased by 4 m. If the length is reduced by 1 m and breadth is increased by 4 m, the area is increased by 89 square metres. Find the dimensions of the rectangle.
Let the length and breadth of rectangle be l and b meters respectively.
area of rectangle = l×b
According to question -
(l + 3)(b - 4) = (l×b) - 67
⇒ lb - 4l + 3b - 12 = lb - 67
⇒ 4l - 3b = 55.....(1)
and,
(l - 1)(b + 4) = (l×b) + 89
⇒ lb + 4l - b - 4 = lb + 89
⇒4l - b = 93.....(2)
Subtracting Equation (1) From equation (2), we get -
b = 19
Substituting the value of b in equation (2), we get -
l = 28
Thus, Length = 28 meters and Breadth = 19 meters.