Correct Option
To determine the shortest distance between the two offices, we must trace the paths of 'A' and 'B' independently and then calculate the Euclidean distance between their final positions.
Both 'A' and 'B' start from the same point and walk 20 m East, then an additional 10 m East together. Their common starting point for individual divergence is therefore 30 m East of the initial house.
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Path of 'A':
- From the common point (30 m East), 'A' turns left (North) and travels 2 m.
- Then, 'A' turns right (East) and travels 12 m to reach his office.
- Relative to the common point, 'A's office is 12 m East and 2 m North.
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Path of 'B':
- From the common point (30 m East), 'B' turns right (South) and travels 8 m.
- Then, 'B' turns left (East) to travel 4 m.
- Subsequently, 'B' turns right (South) and travels 5 m to reach his office.
- Relative to the common point, 'B's office is 4 m East and (8 + 5) = 13 m South.
Now, we determine the relative displacement between the two offices:
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Horizontal displacement (East-West): The Eastward displacement of 'A's office from the common point is 12 m. The Eastward displacement of 'B's office from the common point is 4 m. The difference in Eastward positions is |12 - 4| = 8 m.
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Vertical displacement (North-South): The Northward displacement of 'A's office from the common point is 2 m. The Southward displacement of 'B's office from the common point is 13 m. The total vertical separation is 2 m (North) + 13 m (South) = 15 m.
The shortest distance between the two offices is the hypotenuse of a right-angled triangle formed by these horizontal and vertical displacements. Using the Pythagorean theorem:
Distance² = (Horizontal displacement)² + (Vertical displacement)²
Distance² = 8² + 15²
Distance² = 64 + 225
Distance² = 289
Distance = √289 = 17 m
Incorrect Options
Options 15 m, 19 m, and 20 m are incorrect as they do not result from the accurate calculation of the shortest distance using the Pythagorean theorem based on the given directional movements. A precise application of the path tracing and distance formula yields 17 m.
