Question 3

We need to check if a rectangular mango grove with specific dimensions and area is possible.

Step 1 — Define dimensions and area

Let's assume the breadth of the mango grove. Let the breadth be $x$ meters. The problem states the length is twice its breadth. So, the length will be $2x$ meters. The area of a rectangle is length multiplied by breadth. We can write the area as $x \times 2x$. This simplifies to $2x^2$. The problem gives the area as $800 \text{ m}^2$. We can now set up an equation.

$2x^2 = 800$

Step 2 — Solve for the breadth

We need to solve our equation for $x$. First, let's divide both sides by 2.

$x^2 = \frac{800}{2}$

$x^2 = 400$

Now, we take the square root of both sides.

$x = \pm\sqrt{400}$

$x = \pm 20$

The breadth of a grove cannot be negative. So, we choose the positive value for $x$.

$\boxed{\text{Breadth} = 20 \text{ m}}$

Step 3 — Calculate the length

We know the breadth is 20 meters. The length is twice the breadth. So, we multiply the breadth by 2.

$\text{Length} = 2 \times 20$

$\boxed{\text{Length} = 40 \text{ m}}$

Since we found positive values for both length and breadth, it is possible.

Answer

(i) Yes, it is possible to design such a mango grove. (ii) The length of the mango grove is 40 m. (iii) The breadth of the mango grove is 20 m.