Question

The area of a square field is $9hectares$. A man cycles along its boundary at$18km/h$. In how much time will he return to starting point?

Answer 1

Step 1: Finding the side of the square field

Given

Area of the square field $=9hectare=90000m^2(\sin ce1hectare=10000m^2)$

We know that

$Areaofsquare={\left(side\right)}^2$

Let $a$ be the side of the square.

Then,

$a^2=90000m^2$

So$a=\sqrt{90000}=300m$

Thus, the side of the square is $300m$

Step 2: Finding the perimeter of the square field

We know that,

$\begin{array}{rcl}Perimeterofsquare& =& 4\times side\\ & =& 4\times 300\\ & =& 1200m\end{array}$

Step 3: Finding the time taken to complete the boundary of the field

$\begin{array}{rcl}Speedofman& =& 18km/h\\ & =& 18\times \frac{5}{18}m/s\\ & =& 5m/s\end{array}$

We know that,

$time=\frac{dis\tan ce}{speed}$

So,

Time is taken to cover the distance $1200m$ is

$$\begin{gathered} =\frac{1200}{5} \\ =240seconds \end{gathered}$$

Hence, the man will return to the starting point in $240seconds$.