Question : A man walking at 3 km/hr crosses a square field diagonally in 2 minutes. The area of the field (in square metres) is:
Option 1: 3000
Option 2: 5000
Option 3: 6000
Option 4: 2500
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Correct Answer: 5000
Solution :
A man walking at the speed of 3 km/hr = $3×\frac{5}{18}=\frac{5}{6}$ m/s
The distance covered in 2 min $ = \frac{5}{6}×2×60=100$ m
$\therefore$ Length of the diagonal = 100 m
$\therefore$ Area of the field $ = \frac{1}{2}×(\text{diagonal})^2=\frac{1}{2}×(100)^2 = 5000$ square metres
Hence, the correct answer is 5000.
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