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.

Answer 1

Let the breadth of mango grove be $l$. 
Length of mango grove will be $2l$.
Area of mango grove = 800
$(2l) (l) =800$
$2l^2 =800$
$l^2 = \frac{800}{2}=400$
$l^2-400=0$

Comparing this equation with $al^2 + bl + c = 0$, we obtain 
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