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Quadratic Equations
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30/05/2021 12:13 pm
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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.
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30/05/2021 12:14 pm
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 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.
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