Ans:
Let breadth of rectangular mango grove $=x$ meters
Let length of rectangular mango grove $=2 \mathrm{x}$ meters
Area of rectangle $=$ length $x$ breadth $=x \times 2 x=2 x^{2} m^{2}$
According to given condition: $2 x^{2}=800$ $\Rightarrow 2 x^{2}-800=0$ $\Rightarrow x^{2}-400=0$
Comparing equation $\mathrm{x}^{2}-400=0$ with general form of quadratic equation $a x^{2}+b x+c=0$, we get $a=1, b=0$ and $c=400$
Discriminant $=\mathrm{b}^{2}-4 \mathrm{ac}=(0)^{2}-4(1)(-400)=1600$
Discriminant is greater than 0 means that equation has two distinct real roots. Therefore, it is possible to design a rectangular grove.
Applying quadratic formula, $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ to solve equation.
$$
x=\frac{0 \pm \sqrt{1600}}{2 \times 1}=\frac{\pm 40}{2}=\pm 20
$$
$\therefore x=20,-20$ We discard negative value of $x$ because breadth of rectangle cannot be in negative.
Therefore, $x=$ breadth of rectangle $=20$ meters
Length of rectangle $=2 \times=2 \times 20=40$ meters