Q. 393.9( 7 Votes )

The area of a rectangle gets reduced by 8 m2, when its length is reduced by 5 m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m2. Find the length and the breadth of the rectangle.

Answer :

Let the length and breadth of rectangle be l and b meters respectively.


area of rectangle = l×b


According to question -


(l - 5)(b + 3) = (l×b) - 8


lb + 3l - 5b - 15 = lb - 8


3l - 5b = 7.....(1)


and,


(l + 3)(b + 2) = (l×b) + 74


lb + 2l + 3b + 6 = lb + 74


2l + 3b = 68.....(2)


From equation (1), we get -


l = (5b + 7)/3.....(3)


Substituting the value of l in equation (2), we get -




19b + 14 = 204


19b = 190


b = 10


Substituting the value of b in equation (3), we get -


l = 19


Thus, Length = 19 meters and Breadth = 10 meters.


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