Question

if the length of a rectangle is decreased by 3 metre and its width is increased by 3 metre then the area of rectangle remains same however if its length is increased by 2 metre and its width is decreased by 2 metre then its area is decreased by 10 metre square find the length and breadth of the rectangle​

Answer 1

Step-by-step explanation:

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