Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.

Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove = (2l) (l) = 2l²

2l² = 800

= 0

=

Comparing this equation with al² + bl + c = 0,

we obtain,

a = 1 b = 0, c = 400

Discriminant = b² − 4ac = (0)² − 4 × (1) × (− 400) = 1600

Here, b² − 4ac > 0

Therefore, the equation will have real roots.

And hence, the desired rectangular mango grove can be designed.

However, length cannot be negative.

Therefore, breadth of mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m