Question

A square shape of the park of area$23,104m^2$ is to be enclosed with wire placed at heights $1,2,3,4m$ above the ground. Find the required length of the wire, if its length required for each circuit is $10\%$ greater than the perimeter of the field.

Answer 1

Step 1. Find side of square

We have given that area of square $23104m^2$

Area of square $=sid{e}^2$

$$\begin{gathered} sid{e}^2=23104 \\ side=\sqrt{23104} \\ Side=152 \end{gathered}$$

So, the side of the square is $152m$

Step 2. Now find the perimeter of the square:

The perimeter of the square $=4\times side$

$$\begin{gathered} =4\times 152 \\ =608m \end{gathered}$$

its length required for each circuit is $10\%$ greater than the perimeter of the field.

So the length required is

:$$\begin{gathered} =608\times \frac{110}{100} \\ =608\times \frac{11}{10} \\ =668.8m \end{gathered}$$

Step 4. Now find the total length:

The wire goes around $4times$, so the total length of the wire required:

$$\begin{gathered} =4\times 668.8 \\ =2675.2 \end{gathered}$$

Hence, the required length is $2675.2m$.