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.

Solution:

Let l be the breadth of the mango grove.

And 2l be the length of the mango grove.

Area of the mango grove = (2l) (l)= 2l²

2l² = 800

l² = 800/2 = 400

l² – 400 =0

Comparing the given equation with ax² + bx + c = 0, we get;

a = 1, b = 0, c = 400

As we know, Discriminant = b² – 4ac

=> (0)² – 4 × (1) × ( – 400) = 1600

Here, b² – 4ac > 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