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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.
Given:
Length of the mangrove is twice its breadth and the area is $800\ m^2$.
To do:
We have to find length and breadth of the mangrove if it is possible to design with the given conditions.
Solution:
Let the breadth of the rectangular mangrove be $x$ m.
This implies,
The length of the rectangular mangrove$=2x$ m.
According to the question,
$x \times (2x)=800$
$2x^2=800$
$x^2=400$
$x^2=(20)^2$
$x=\pm 20$
Length cannot be negative. Therefore, breadth of the mangrove$=20\ m$.
$2x=2(20)=40\ m$
The breadth of the mangrove is $20\ m$ and the length of the mangrove is $40\ m$.
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