Question

a boy is cycling along a square field at the speed of 18 km/hr. in how much time will he complete 5 rounds if the area of square field is 9604 m²?

Explanation:

Step1: Find the side - length of the square field

The area of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 9604\ m^{2}$, then $s=\sqrt{9604}=98\ m$.

Step2: Calculate the perimeter of the square field

The perimeter of a square is $P = 4s$. Substituting $s = 98\ m$, we get $P=4\times98 = 392\ m$.

Step3: Calculate the distance covered in 5 rounds

The distance covered in 5 rounds is $d = 5P$. So $d=5\times392=1960\ m$. Convert the speed from $km/h$ to $m/s$. Since $1\ km = 1000\ m$ and $1\ h=3600\ s$, the speed $v = 18\ km/h=\frac{18\times1000}{3600}=5\ m/s$.

Step4: Calculate the time taken

We know that time $t=\frac{d}{v}$. Substituting $d = 1960\ m$ and $v = 5\ m/s$, we get $t=\frac{1960}{5}=392\ s$.

Answer:

$392\ s$