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.
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 this equation with al2 + bl + c = 0, we get
a = 1, b = 0, c = 400
Discriminant = b2 - 4ac = (0)2 - 4 × (1) × ( - 400) = 1600
Here, b2 - 4ac > 0
Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.
l = ±20
However, length cannot be negative.
Therefore, breadth of mango grove = 20 m
Length of mango grove = 2 × 20 = 40 m
Let the breadth of the rectangular mango grove be x meter and the length 2x meters. Then
Area of the rectangle
length x breadth = 800
x(2x) = 800
2x2 = 800
x2 = 400
Sides of the rectangular hall never be negative
= 2x = 2(20) = 40
Yes, it is possible.
Hence, breadth of the hall be 20 meters and length be 40 meters.