Question

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is $800m^2$? If so, find its length and breadth.

Answer 1

Step $1$: Make a mathematical equation using giving conditions :

Let the length of the rectangular grove is $l$ and the breadth of the rectangular grove is $b$ .

Given: length is twice its breadth, the area is $800m^2$.

Length$\left(l\right)=2b$

We know that Area $\left(A\right)$ of the rectangle is given by :

$$\begin{gathered} A=l\times b \\ \Rightarrow A=2b\times b \\ \Rightarrow 800=2b^2 \\ \Rightarrow b^2=400 \\ \Rightarrow b^{}=\pm 20 \end{gathered}$$`

Step $2$: Compute the length and breadth of the park :

We know that, the value of the sides cannot be negative.

Breadth $\left(b\right)=20m$

Length $\left(l\right)=2\left(20\right)$

Length $\left(l\right)=40m$

Hence, the length of the rectangular mango grove is $40m$ and the breadth of the rectangular mango grove is $20m$.