Question

Question 3
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is $800m^2$? If so, find its length and breadth.

Answer 1

Let the breadth of mango grove be l.
Length of mango grove will be 2l.
Area of mango grove $=\left(2l\right)\left(l\right)=2l^2$
$\Rightarrow$ $2l^2=800$
$\Rightarrow$$l^2=\frac{800}{2}=400$
$\Rightarrow$ $l^2-400=0$
Comparing this equation with $a{x}^2+bx+c=0$, we get
$a=1,b=0,c=400$
$Discriminant=b^2-4ac$
$=(0{)}^2-4\times (1)\times (-400)=1600$
$Here,b^2-4ac>0$
Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.
$l^2-400=0$
$\Rightarrow$$l=\pm 20$
However, length cannot be negative.
Therefore, breadth of mango grove = 20 m
Length of mango grove $=2\times 20=40m$