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 breadth be x meters and so length is 2x meters.

By formula,

Area = Length × Breadth

⇒ 800 = 2x.x

⇒ 2x² = 800

⇒ x² = $\dfrac{800}{2}$

⇒ x² = 400

⇒ x² - 400 = 0.

Comparing x² - 400 = 0 with ax² + bx + c = 0, we get :

a = 1, b = 0 and c = -400.

Substituting value in b² - 4ac, we get :

⇒ 0² - 4 × 1 × -400

⇒ 0 + 1600

⇒ 1600.

Since, b² - 4ac > 0,

∴ Equation has real and distinct roots.

Solving, x² - 400 = 0, we get :

⇒ x² = 400

⇒ x = $\sqrt{400}$

⇒ x = ± 20

Since, side cannot be negative.

∴ x ≠ -20.

∴ Breadth (x) = 20 meters and Length (2x) = 2 × 20 = 40 meters.

Hence situation is possible and length = 40 meters and breadth = 20 meters.