Question

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.

Answer 1

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`

l² = 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

Answer 2

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

x = `sqrt400`

x = `+-20`

Sides of the rectangular hall never be negative.

Therefore, length

2x = 2(20) = 40

Yes, it is possible.

Hence, breadth of the hall be 20 meters and length be 40 meters.