Question

If the length of a rectangle is increased by 7 units and the breadth is decreased by 3 units, its area does
not change. If the length of the rectangle is decreased by 7 m and breadth is increased by 5 m, are
remains unaffected. Find the length and breadth of the rectangle.
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Answer 1

Answer:

The area of a rectangle remains the same if the lengthis increased by 7 metres and the breadth is decreased by 3 meters. The area remains unaffected if the length isdecreases by 7 metres andbreadth is increased by 5metres.

Answer 2

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+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