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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.
Solution 1
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`
l2 = 400
l2 - 400 = 0
Comparing this equation with al2 + bl + c = 0, we get
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
Solution 2
Let the breadth of the rectangular mango grove be x meter and the length 2x meters. Then
Area of the rectangle
length x breadth = 800
x(2x) = 800
2x2 = 800
x2 = 400
x = `sqrt400`
x = `+-20`
Sides of the rectangular hall never be negative.
Therefore, length
2x = 2(20) = 40
Yes, it is possible.
Hence, breadth of the hall be 20 meters and length be 40 meters.
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