# 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

2
by danuj

2014-10-14T20:43:45+05:30
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 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
length=40-b=40-10 meter=30 meter.
Ans:The length and breadth of the field are 30 m and 10 m respectively.
2014-10-14T21:43:52+05:30

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Let the length of the field = x
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)
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

Hence length = 30m