Question 3:
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.
Answer:
Let the breadth of mango grove be l.
Length of mango grove will be 2l.
Area of mango grove = (2l) (l) = = 2l2
2l2 = 800
l2 = 800/2 = 400
l2 − 400 = 0
Comparing this equation with al2 + bl + c = 0, we obtain a = 1 b = 0, c = 400
Discriminant = b2 − 4ac = (0)2 − 4 × (1) × (− 400) = 1600
Here, b2 − 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
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