Question

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

Answer 1

1 hectare = 0.01 km²
∴ 8 hectares = 0.08 km²
Area of the square field = $\frac{1}{2}{d}^2$ (where d is the diagonal of the square)
$$\begin{gathered} \Rightarrow 0.08=\frac{1}{2}{d}^2 \\ \Rightarrow d^2=0.16 \\ \Rightarrow d=0.4\mathrm{km} \end{gathered}$$

Or,
d = 400 m

Now,

​$$\begin{gathered} \mathrm{Speed}=4\mathrm{km}/\mathrm{h} \\ =\frac{4\times 1000}{3600} \\ =\frac{10}{9}\mathrm{m}/\sec \end{gathered}$$

We know:
$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

$$\begin{gathered} \Rightarrow \frac{10}{9}=\frac{400}{\mathrm{Time}} \\ \Rightarrow \mathrm{Time}=360\sec \\ =\frac{360}{60} \\ =6\min \end{gathered}$$

A man would take 6 minutes to walk across the field diagonally.