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

Answer:

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+7)×(y−3)=xy

and(x−7)×(y+5)=xy

(x+7)×(y−3)=xy

=>xy−3x+7y−21=xy

=>−3x+7y−21=0

=>7y=3x+21....(i)

Also,(x−7)×(y+5)=xy

=>xy+5x−7y−35=xy

=>5x−7y−35=0....(ii)

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

5x−7y−35=0

=>5x−3x−21−35=0

=>2x=56

=>x=28

Substituting x=28 in equation (i), we get,

7y=3x+21

=>7y=3(28)+21

=>7y=105

=>y=

7

105

Therefore, length of rectangle =x=23 metres

and breadth of rectangle =y=15 metres