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 $40\ m$.