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Question

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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Solution

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=8002=400
l2400=0
Comparing this equation with ax2+bx+c=0, we get
a=1,b=0,c=400
Discriminant=b24ac
=(0)24×(1)×(400)=1600
Here, b24ac>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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