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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.

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.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Dear Student

Let the breadth of mango grove bel.
Length of mango grove will be 2l.
Area of mango grove = (2l) (l)= 2l^2

2l^2= 800

l^2= 800/2 = 400
l^2- 400 =0
Comparing the given equation withax^2+bx+c= 0, we get

a= 1,b= 0,c= 400
As we know, Discriminant =b^2- 4ac
=> (0)^2- 4 × (1) × ( - 400) = 1600
Here,
b^2-4ac>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, breadth of mango grove = 20 m
Length of mango grove = 2 × 20 = 40 m


Thanks

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