The area of a rectangle increases by 8 m² if its length is increased by 5 m and breadth is decreased by 7 m. If the length is decreased by 5 m and breadth is increased by 8 m, then its area increases by 33 m². What is the perimeter of the original rectangle (in m)?

Correct option is D

Given:

The area of a rectangle increases by 8 m² if its length is increased by 5 m and breadth is decreased by 7 m.
If the length is decreased by 5 m and the breadth is increased by 8 m, then its area increases by 33 m².
Formula Used:
Area of a rectangle = Length × Breadth
Perimeter of a rectangle = 2 × (Length + Breadth)
Solution:
Let the original length be l meters and the original breadth be b meters.
According to the first condition:
New length = l + 5
New breadth = b - 7
New area = (l + 5) × (b - 7)
Original area = l × b
New area = Original area + 8
=> (l + 5) (b - 7)= lb + 8
=> lb − 7l + 5b − 35 = lb + 8
=> − 7l + 5b = 43...(i)
According to the second condition:
New length = l − 5
New breadth = b + 8
New area = (l − 5) × (b + 8)
Original area = l × b
New area = Original area + 33
=> (l − 5)(b + 8) = lb + 33
=> lb +8l − 5b − 40 = lb + 33
=> 8l − 5b  = 73...(ii)
Solving equations (i) and (ii):
Add both equations to eliminate b:
(-7l + 5b) + (8l - 5b) = 43 + 73
l = 116
Now substitute l = 116 into equation (1):
-7(116) + 5b = 43
-812 + 5b = 43
5b = 43 + 812
5b = 855
b = 855 / 5 = 171
P = 2(l + b)
P = 2(116 + 171) = 2(287) = 574