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