Question

the length of a rectangular field is increased by 3 and breadth is decreased by 3 .Then the area decreased by 18 m square but if length and breadth both are increased by 3 its area is increased by 60 square find the length and breadth of the field​

Answer 1

Answer:

The length of the rectangle is= 10m

The breadth of the rectangle is= 7m

Step-by-step explanation:

Let the length of the original rectangle is = x m

And the breadth of the original rectangle is = y m

Now the area of the rectangle is = x×y m^2

Now if the length of the rectangle is increase d by 3 m then the length of the rectangle is

= x+3 m

And if the breadth of the rectangle is decreased by 3 m then the breadth of the rectangle is = y-3 m

Now the area of the rectangle is = (x+3) × (y-3) m^2

Now by given condition,

(x+3) ×(y-3) = xy-18

=> xy-3x+3y-9 = xy-18

=> -3x+3y = -18+9=-9

=> 3x-3y = 9----(1)

Now, if the length of the rectangle is increased by 3m then the length of the rectangle is = x+3 m

And if the breadth of the rectangle is increased 3m then the breadth of the rectangle is = y+3 m

Now the area of the rectangle is = (x+3) × (y+3) m^2

Now by given condition,

(x+3) ×(y+3) = xy+60

=> xy+3x+3y+9 = xy+60

=> 3x+3y = 51-----(2)

Now solving (1) and (2), we get

(1) +(2),

3x-3y+3x+3y = 9+51

=> 6x = 60

=> x= 10

Now, 3x+3y = 51

=> 3y = 51-3y = 51-3×10 =51-30 = 21

=> y =21/3 = 7

So, the length of the rectangle is= 10 m

Breadth of the rectangle is= 7 m