Question

The perimeter of a rectangular field is 80 m. If the length of the field is decreased by 2 m and its breadth
increased by 2 m, the area is increased by 36 m. Find the length and the breadth of the rectangular field

Answer 1

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

THANKS FOR ALERTING ME

PLS MARK BRAINLIEST

Answer 2

Answer:

Let length be 'x' and Breadth 'y'.

2(x+y)=80    [ Perimeter=2(l+b) ]

= x+y=40 ----- (1)

(x-2)(y+2)=xy+36 [ Area=xy ]

= xy+2x-2y-4=xy+36

= x-y=20 -------(2)

Adding (1) and (2), we get

2x=60

x=30m

y=10m

Length of the field is 30m and Breadth of the field is 10m