Question

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

Answer 1

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.

Answer 2

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

Hence length = 30m
         breadth = 10m