This is the basic question from linear equations in two variables as it was already asked in various examinations in which we have been asked to find the length and breadth of rectangle if it is given that the area of a rectangle gets reduced by 67 square units, if its length is increased by 3 and breadth decreased by 4. If length is reduced by 1 and breadth increased by 4 then the area increases by 89 square units.

RS Aggarwal, Class 10, chapter 3E, question no 40

## Let the length of the rectangle be x metres and the breadth be y metres.

Area of the rectangle=length×breadth

=x×y=xy sq. metres

From the given information, we have,

(x+3)×(y−4)=xy−67and(x−1)×(y+4)=xy+89(x+3)×(y−4)=xy−67=>xy−4x+3y−12=xy−67=>4x−3y=55=>4x=3y+55....(i)Also,(x−1)×(y+4)=xy+89=>xy+4x−y−4=xy+89=>4x−y=93....(ii)

Substituting equation (i) in equation (ii), we get,

4x−y=93=>3y+55−y=93=>2y=38=>y=19

Substituting y=19 in equation (i), we get,

4x=3y+55=>4x=3(19)+55=>4x=112=>x=28

Therefore, length of rectangle =x=28 metres

breadth of rectangle =y=19 metres