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.

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Let the breadth of the rectangular mango grove be x m
So, length = ‘2’ m
According to question,
Area = 800
⇒ 2x(x) = 800
⇒ 2x² = 800
⇒ x² = 400
⇒ x² – 400 = 0
⇒ x² + 0x – 400 = 0
Here, a = 1, b = 0, c = – 400
D = b² – 4ac
= 0 – 4(1) (–400)
= 1600
So, the given quadratic equation has real roots (∵ D > 0) and hence it is possible to design rectangular mango grove.
Now, solving the quadratic equation x² + 0x – 400 = 0, by quadratic formula, we get,

                     

              
              
∵                is not possible
So,              
Hence, breadth of the rectangular mango grove is 20 m and length is 40 m.