The area of rectangle gets reduced by 50 sq. units. If its length is reduced by 5 unit and the breadth is increased by 2 unit. If we increase the length by 10 units and breadth decreased by 5 units, then the area remains same. Find the length and breadth of the rectangle.

Step-by-step explanation:

Let the length and breadth of the rectangle be a, b units respectively.

Then the area will be ab square units.

Now if the length of the rectangle is reduced by 5 units and breadth is increased by 2 units then new length and breadth will be (a-5) units and (b+2) units.

Then new area will be (a-5) (b+2).

Then according to the problem,

(a-5) (b+2) - ab=-80

or, 2a-5b=-70 ... (1).

Now if length of the rectangle is increased by 10 units and breadth is decreased by 5 units then new length and breadth will be (a+10) units and (b-5) units.

Then new area will be (a+10) (b-5).

Then according to the problem,

(a+10) (b-5) - ab=50

or, 10b-5a=100

or, 2b-a=20

or, 4b-2a=40 ... (2).

Now adding (1) and (2) we get

-b=-30

or, b=30.

Putting the value of b in (1) we get, a=40.

Now a+b=40+30=70.