Question

The area of a rectangular field is 2000 sq.m and its perimeter is 180m. form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. the length and breadth are

Answer 1

heres your answer bro

Answer 2

Given :

The area of a rectangular field is 2000 sq meters

The perimeter of rectangular field = 180 meters

The length of field = x m

To Find :

The length and The breadth of field

Solution :

As The length of field = x meters

Let The breadth of field = y meters

Now,

∵  Area of a rectangular field = Length × breadth

So,  2000 m² = Length × breadth

Or,   x × y = 2000 m²       ..........1

Again

∵  Perimeter of rectangular field = 2 × ( length + breadth )

Or,  180 m = 2 × ( x + y )

Or,   x + y = $\dfrac{180 m}{2}$

∴     x + y = 90 meters               ...........2

Now,  ( x - y ) ² = ( x + y )² - 4 x y

                        =  ( 90)² - 4 × 2000

                        = 8100 - 8000

                        = 100

∴   ( x - y ) ² = 100

Or,  x - y = $\sqrt{100}$

i.e  x - y = 10              ...............3

From eq 2 and eq 3

      ( x + y ) + ( x - y ) = 90 + 10

Or,  ( x + x ) + ( y - y ) = 100

Or,   2 x + 0 = 100

∴        x = $\dfrac{100}{2}$ = 50 m

i.e   Length of field = x = 50 m

Put the value of x into eq 2

∵    x + y = 90

Or,    50 + y = 90

Or,      y = 90 - 50

∴        y = 40 m

i.e breadth of field = y = 40 m

Hence , The length of rectangular field is 50 meters

And The breadth of rectangular field is 40 meters  . Answer