# Q3.    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.

D Divya Prakash Singh

Let the breadth of mango grove be $'b'$.

Then the length of mango grove will be $'2b'$.

And the area will be:

$Area = (2b)(b) = 2b^2$

Which will be equal to $800m^2$ according to question.

$\Rightarrow 2b^2 = 800m^2$

$\Rightarrow b^2 - 400 = 0$

Comparing to get the values of $a,b,c$.

$a=1, \ b= 0 , \ c = -400$

Finding the discriminant value:

$D = b^2-4ac$

$\Rightarrow 0^2-4(1)(-400) = 1600$

Here, $D>0$

Therefore, the equation will have real roots.

And hence finding the dimensions:

$\Rightarrow b^2 - 400 = 0$

$\Rightarrow b = \pm 20$

As negative value is not possible, hence the value of breadth of mango grove will be 20m.

And the length of mango grove will be: $= 2\times10 = 40m$

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