Question

The area of a square field is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?

Answer 1

We know that 1 hectare = 10000 m².
So, Area of square field = 8 hectares = 80000 m².
$$\begin{gathered} \Rightarrow \frac{1}{2}{\left(\mathrm{diagonal}\right)}^2=80000 \\ \Rightarrow {\left(\mathrm{diagonal}\right)}^2=160000 \\ \Rightarrow \mathrm{diagonal}=\sqrt{160000}=400\mathrm{m}. \end{gathered}$$
Now, distance to be travelled = 400 m
speed is given to be 4 km/h = $4\times \frac{1000\mathrm{m}}{60\min }=\frac{4000}{60}\mathrm{m}/\min =\frac{200}{3}\mathrm{m}/\min$
Therefore, $\mathrm{time}\mathrm{taken}=\frac{\mathrm{distance}}{\mathrm{speed}}=\frac{400}{{\displaystyle \frac{200}{3}}}=\frac{400\times 3}{200}=6\mathrm{minutes}.$