Question

56. The area of a rectangle remains unaltered when its length is increased by 6 metre and its breadth is reduced by 3 metre. The perimeter of the rectangle is 36 metre. The area of the rectangle is
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Answer 1

Answer:

let the length of the rectangle is x m

breadth is y m

then area=x.y sq m

again when length is (x+6) m and breadth is

(y-3) m then area (x+6)(y-3) is unaltered

so,

(x+6)(y-3)=xy

=> xy+6y-3x-18=xy

=> 6y-3x=18

=> 3(2y-x)=18

=> 2y-x=18/3

=> 2y-x=6

=> x=2y-6

again perimeter=2(x+y)=36

=> x+y=36/2

=> x+y=18

=> 2y-6+y=18

=> 3y=18+6

=> 3y=24

=> y=24/3

=> y=8

x=2y-6=2.8-6=16-6=10

so length of the rectangle is 10 m and breadth is 8 m.

so area is 10×8sq m=80 sq m