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.
Yes. Length = 40 m, Breadth = 20 m
Step 1: Define the variables.
Let the breadth of the rectangular mango grove be \(b\) metres.
Then, according to the question, the length is twice the breadth, so:
\[\text{Length} = 2b\]
Step 2: Use the area condition.
Area of a rectangle = length × breadth.
We are given that the area is 800 m². So:
\[\text{Area} = (\text{Length}) \times (\text{Breadth}) = 2b \times b = 800\]
That is,
\[2b^2 = 800\]
Step 3: Form and solve the equation.
Divide both sides by 2:
\[b^2 = 400\]
Take square roots of both sides:
\[b = \pm 20\]
Since breadth is a physical length, it must be positive, so:
\[b = 20\,\text{m}\]
Step 4: Find the length.
Length = \(2b = 2 \times 20 = 40\,\text{m}\).
Step 5: Check if the design is possible.
Check the area with these dimensions:
\[\text{Area} = 40 \times 20 = 800\,\text{m}^2\]
The condition is satisfied.
Conclusion: Yes, such a rectangular mango grove is possible. The breadth is 20 m and the length is 40 m.