Question

What will be the cost of fencing a rectangular compound if the wire cost $\mathrm{Rs}.20$ per meter? Also, the area is $40{\mathrm{m}}^2$ and $\mathrm{length}=2\times \mathrm{breadth}$?

Answer 1

Step 1. Calculate the length and breadth of the rectangular compound.

Let us consider the length and breadth of rectangular compound be $l$ and $b$respectively.

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{rectangular}\mathrm{compound}=40{\mathrm{m}}^2 \\ \Rightarrow l\times b=40 \\ \Rightarrow 2b\times b=40\left[\because l=2b\right] \\ \Rightarrow b^2=20 \\ \Rightarrow b=\sqrt{20} \\ \therefore b=2\sqrt{5}\mathrm{m} \end{gathered}$$

Substitute the value of $b$ in given relation:

$$\begin{gathered} \mathrm{length}=2\times \mathrm{breadth} \\ =2\times 2\sqrt{5} \\ =4\sqrt{5}\mathrm{m} \end{gathered}$$.

Step 2. Calculate the cost of fencing.

$$\begin{gathered} \mathrm{Perimeter}=2(l+b) \\ =2(4\sqrt{5}+2\sqrt{5}) \\ =2\times 6\sqrt{5} \\ =12\sqrt{5}\mathrm{m} \end{gathered}$$

Since the cost of wire is $\mathrm{Rs}.20$ per meter.

$$\begin{gathered} \therefore \mathrm{The}\mathrm{cost}\mathrm{of}\mathrm{fencing}=20\times 12\sqrt{5} \\ =240\sqrt{5} \\ =\mathrm{Rs}.536.65 \end{gathered}$$

Hence, the cost of fencing is $\mathrm{Rs}.536.65$.