Square field via diagonal crossing A man walking at 3 km/h crosses a square field along the diagonal in 2 minutes. What is the area of the field (approximately, in acres)?
Correct Answer: ≈ 1.24 acres
Introduction / Context:When crossing a square field along its diagonal at uniform speed, the walking distance equals the diagonal length. From the diagonal, we can find the side and thus the area. Convert units consistently and, if asked in acres, convert from square meters (or hectares) at the end.
Given Data / Assumptions:
- Speed = 3 km/h.
- Time = 2 minutes = 2/60 h.
- 1 acre = 4046.856 m^2.
Concept / Approach:Distance = speed * time. For a square with side s and diagonal d, d = s * sqrt(2). Then area = s^2. Convert meters to acres.
Step-by-Step Solution:
Distance walked (diagonal) = 3 * (2/60) = 0.1 km = 100 mSide s = d / sqrt(2) = 100 / 1.4142 ≈ 70.71 mArea = s^2 ≈ (70.71)^2 ≈ 5000 m^2In acres = 5000 / 4046.856 ≈ 1.235 acres ≈ 1.24 acresVerification / Alternative check:In hectares: 5000 m^2 = 0.5 ha. 0.5 ha equals ≈ 1.2355 acres, confirming the conversion.
Why Other Options Are Wrong:0.50 and 0.75 acres are too small; 2.00 acres is too large for a 100 m diagonal.
Common Pitfalls:Using the side instead of the diagonal as the 100 m distance, or failing to convert time to hours before multiplying by speed.
Final Answer:≈ 1.24 acres