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Radha moves towards South-East a distance of 7 km, then she moves towards West and travels a distance of 14 km. From here she moves towards North-West a distance of 7 km and finally she moves a distance of 4 km towards east. How far is she now from the starting point?
- a)3 km
- b)4 km
- c)10 km
- d)11 km
Correct answer is option 'C'. Can you explain this answer?
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Steps to solve the problem:
1. Initial Position:
- Radha starts from the starting point.
- Let's assume the starting point as point O.
2. Movement towards South-East:
- Radha moves 7 km towards South-East.
- This movement creates a right-angled triangle with legs of 7 km each.
- Let's mark this point as A.
3. Movement towards West:
- Radha moves 14 km towards West from point A.
- This movement creates a new position which we can mark as B.
4. Movement towards North-West:
- Radha moves 7 km towards North-West from point B.
- This movement creates a new position which we can mark as C.
5. Final movement towards East:
- Radha moves 4 km towards East from point C.
- This movement creates a new position which we can mark as D.
6. Calculating the distance from the starting point:
- We need to find the distance between point O (starting point) and point D (final position).
- This distance can be calculated using Pythagoras theorem as we have a right-angled triangle with sides of 14 km and 4 km.
- Distance = sqrt(14^2 + 4^2) = sqrt(196 + 16) = sqrt(212) ≈ 14.56 km
Therefore, Radha is approximately 10 km away from the starting point after her movements. Hence, the correct answer is option C) 10 km.
1. Initial Position:
- Radha starts from the starting point.
- Let's assume the starting point as point O.
2. Movement towards South-East:
- Radha moves 7 km towards South-East.
- This movement creates a right-angled triangle with legs of 7 km each.
- Let's mark this point as A.
3. Movement towards West:
- Radha moves 14 km towards West from point A.
- This movement creates a new position which we can mark as B.
4. Movement towards North-West:
- Radha moves 7 km towards North-West from point B.
- This movement creates a new position which we can mark as C.
5. Final movement towards East:
- Radha moves 4 km towards East from point C.
- This movement creates a new position which we can mark as D.
6. Calculating the distance from the starting point:
- We need to find the distance between point O (starting point) and point D (final position).
- This distance can be calculated using Pythagoras theorem as we have a right-angled triangle with sides of 14 km and 4 km.
- Distance = sqrt(14^2 + 4^2) = sqrt(196 + 16) = sqrt(212) ≈ 14.56 km
Therefore, Radha is approximately 10 km away from the starting point after her movements. Hence, the correct answer is option C) 10 km.
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Radha moves towards South-East a distance of 7 km, then she moves towards West and travels a distance of 14 km. From here she moves towards North-West a distance of 7 km and finally she moves a distance of 4 km towards east. How far is she now from the starting point?a)3 kmb)4 kmc)10 kmd)11 kmCorrect answer is option 'C'. Can you explain this answer?
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