Question

The perimeter of a rectangular field is 140m. If the length of the field is increased by 2m and its breadth is decreased by 3m then the area is decreased by 66 sq m. Find its length and breadth?

I will mark you as BRAINLIEST if you answer this.

Answer 1

Answer:

Length=40m Breadth=30m

Step-by-step explanation:

Firstly Perimeter is 140

Let x be length and y be breadth

2x+2y=140

x+y=70

x=70-y

Take the value of x,

Now,

After legth is increased by 2 amd breadth is decreased by 3 area decreases by 66,

So,

(x+2)*(y-3)=z-66

where z is previous area, i.e., z=x*y

So,

xy+2y-3x-6=xy-66

2y-210+3y-6=-66 (Substituting value of x)

5y=210-60

y=150/5

y=30

x=70-y

x=40

Answer 2

Let the length of the field = x

breadth = y

perimeter = 2(x+y) =140

⇒ x+y = 140/2

⇒ x+y = 70

Area = xy

If the length is increased by 2m and breadth is decreased by 3m,

new length = (x+2)

new breadth = (y-3)

area = (x+2)(y-3) = xy-3x×2y-6

this area is 36 m² more than earlier area. So

( xy-3x×2y-6)- (xy) = 160

Add the 2 equations, we get

⇒ x = 30m

y = 40cm

Hence length = 30m

breadth = 40cm