Question

the area of a rectangle remains the same if the length is increased by 7m and the breadth is decreased by 3m. the area remains unaffected if the length is decreased by 7m and the breadth is increased by 5m. find the dimensions of the rectangle ​

Answer 1

Step-by-step explanation:

let length be x

and breadth be y

1)length increased by 7m=x+7

breadth decreases by 3m =y-3

area remains same ,area of rectangle =length ×breadth

=(x+7)(y-3)

2)length decreases by 7m= x-7

breakup increases by 5m =y+5

area remains same, area=(x-7)(y+5)

we have to equal the both areas

(x+7)(y-3)=(x-7)(y+5)

xy-3x+7y-21=xy-7y+5x-35

14y-8x+14=0

7y-4x+7=0

we have to put x and y values according to option

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= 105/7

Therefore, length of rectangle =x=23 metres

and breadth of rectangle =y=15 metres

hope it help

√\________Anushka❤❤