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The perimeter of a rectangular field is 80 meters if the lenth of the field is decreased by 2 meters and its breadth is increased by 2 meters the area is

increased by 36sq.m find the length and breadth of the rectangular field

Let the length be l meters and let the breadth be b meters. Then,2(l+b)=80 or,l+b=40 or,l=40-b..............................................(1) Area=lb m² New length=(l-2) m New breadth=(b+2) m New area=(l-2)(b+2) m² =lb+2l-2b-4 Given, lb+36=lb+2l-2b-4 or,36=2l-2b-4 or,40=2l-2b or,20=l-b putting the value of l as 40- b from ...(1),we get 20=(40-b)-b or,20-40=-b-b or,-20=-2b or,b=-20/-2=10 Therefore, breadth=10 meter and length=40-b=40-10 meter=30 meter. Ans:The length and breadth of the field are 30 m and 10 m respectively.

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Let the length of the field = x breadth = y perimeter = 2(x+y) =80 ⇒ x+y = 80/2 ⇒ x+y = 40 Area = xy

If the length is decreased by 2m and breadth is increased by 2m, new length = (x-2) new breadth = (y+2) area = (x-2)(y+2) = xy + 2x -2y - 4 this area is 36 m² more than earlier area. So (xy + 2x -2y - 4) - (xy) = 36 ⇒2x -2y - 4 =36 ⇒2x - 2y = 36+4 = 40 ⇒ x-y = 20

Add the 2 equations, we get 2x = 60 ⇒ x = 30m y = 10m