**Solution:**

Let *l* be the breadth of the mango grove.

And 2*l* be the length of the mango grove.

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

2*l*^{2 }= 800

*l*^{2 }= 800/2 = 400

*l*^{2 }– 400 =0

Comparing the given equation with *ax*^{2} + *bx *+ *c* = 0, we get;

*a* = 1, *b* = 0, *c* = 400

As we know, Discriminant = *b*^{2} – 4*ac*

=> (0)^{2} – 4 × (1) × ( – 400) = 1600

Here, *b*^{2} – 4*ac* > 0

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

*l *= ±20

As we know, the value of length cannot be negative.

Therefore, the breadth of the mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m