#### Question

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^{2}? If so, find its length and breadth.

#### Solution 1

Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove = (2l) (l)= 2l^{2}

2l^{2} = 800

l^{2} = 800/2 = 400

l^{2} - 400 =0

Comparing this equation with al^{2} + bl + c = 0, we get

a = 1, b = 0, c = 400

Discriminant = b^{2} - 4ac = (0)^{2} - 4 × (1) × ( - 400) = 1600

Here, b^{2} - 4ac > 0

Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.

l = ±20

However, length cannot be negative.

Therefore, breadth of mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m

#### Solution 2

Let the breadth of the rectangular mango grove be *x *meter and the length 2x meters. Then

Area of the rectangle

length x breadth = 800

x(2x) = 800

2x2 = 800

x2 = 400

`x=sqrt400=+-20`

Sides of the rectangular hall never be negative

Therefore, length

= 2x = 2(20) = 40

Yes, it is possible.

Hence, breadth of the hall be 20 meters and length be 40 meters.