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Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 \[{m^2}\]? If so, find its length and breadth.
(a). Yes. 30m, 50m
(b). Yes. 40m, 20m
(c). Yes. 80m, 40m
(d). No, it is not possible

Last updated date: 25th Jul 2024
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Hint: Write the equations relating the length and the breadth of the mango grove and then solve for its length and breadth. If the answer is feasible, then, it is possible to design.

Complete step-by-step answer:
Let the length of the mango grove be l and its breath be b.

It is given that the length of the mango grove is twice its breadth, hence, we have the relation:
\[l = 2b.............(1)\]

We know that the area of a rectangular object is a product of its length and breadth. Hence, area if the rectangular mango grove is given as follows:
\[A = lb...........(2)\]

The area of the rectangular mango grove is given as 800 \[{m^2}\]. Therefore, from equation (2), we have:
\[800 = lb\]

Substituting equation (1) into the above equation, we have:
\[800 = (2b)b\]

We know simplify the right-hand side of the equation, to get:
\[800 = 2{b^2}\]

Taking 2 to the other side and dividing with 800, we get 400.
\[400 = {b^2}\]

We know that the square root of 400 is 20. Hence, we have:
\[b = 20\]

Using equation (1), we obtain the length of the grove as:
\[l = 2 \times 20\]
\[l = 40\]

Hence, the length of the grove is 40m and the breadth of the grove is 20m.
It is a feasible solution. Hence, we can design such a mango grove with given conditions.

Hence, the correct answer is option (b).

Note: When taking a square root we get both positive and negative roots, choose only the feasible solution, in this case, breadth and length are positive quantities.