Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q3 Download this solution
3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800
. If so, find its length and breadth.
Solution:
Let breadth of rectangular mango grove =
metres
Let length of rectangular mango grove =
metres
Area of rectangle = length x breadth =
=
According to given condition we have:
Comparing equation,
with general form of quadratic equation
, we get
and
Discriminant >0 means that equation has two disctinct real roots. Therefore, it is possible to design a rectangular grove.
{We can directly solve this equation and we get
}. Lets solve it using quadratic formula.
Applying quadratic formula,
to solve equation, we get
We discard negative value of
because breadth of rectangle cannot be in negative.
Therefore,
= breadth of rectangle = 20 metres
Length of rectangle =
metres
Therefore, length of rectangle = 40 metres
And, Breadth of rectangle = 20 metres
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