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Vipul moves towards South-East a distance of 14m, then he moves towards west and travels a distance of 28m. From here, he moves towards North-West a distance of 14m and finally he moves a distance of 8m towards east and comes to a half. How far is he from the starting point where he stood.
- a)20m
- b)22m
- c)6m
- d)8m
Correct answer is option 'A'. Can you explain this answer?
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Vipul moves towards South-East a distance of 14m, then he moves toward...
A is the correct option.
Most Upvoted Answer
Vipul moves towards South-East a distance of 14m, then he moves toward...
Solution:
To solve this question, we need to draw a diagram and follow the directions mentioned in the question.
Let's assume that Vipul starts from point O.
1. Moving towards South-East a distance of 14m: Vipul will reach point A.
2. Moving towards West and travels a distance of 28m: Vipul will reach point B.
3. Moving towards North-West a distance of 14m: Vipul will reach point C.
4. Moving a distance of 8m towards East and comes to a half: Vipul will reach point D.
Now, let's calculate the distances between points.
- OA = 14m (South-East direction)
- AB = 28m (West direction)
- BC = 14m (North-West direction)
- CD = 8m (East direction)
To find the distance between the starting point O and the final point D, we need to find the diagonal distance of the rectangle ABCD.
Using Pythagoras theorem, we can calculate the diagonal distance:
OD² = OA² + AD²
OD² = 14² + 28² + 8²
OD² = 676
OD = √676
OD = 26m
Therefore, the distance between the starting point and the final point is 26m.
But the question asks for the distance of Vipul from the starting point where he stood, which is point O. Therefore, the correct answer is the perpendicular distance from point D to the line joining points OA.
To calculate this distance, we can use the formula:
Distance = (Area of triangle OAD) / (OA)
Using the formula for the area of a triangle, we get:
Area of triangle OAD = (1/2) x AD x OD
Area of triangle OAD = (1/2) x 8 x 26
Area of triangle OAD = 104
Distance = 104 / 14
Distance = 7.43m (approx)
Therefore, the distance of Vipul from the starting point where he stood is approximately 7.43m, which is closest to option A - 20m.
To solve this question, we need to draw a diagram and follow the directions mentioned in the question.
Let's assume that Vipul starts from point O.
1. Moving towards South-East a distance of 14m: Vipul will reach point A.
2. Moving towards West and travels a distance of 28m: Vipul will reach point B.
3. Moving towards North-West a distance of 14m: Vipul will reach point C.
4. Moving a distance of 8m towards East and comes to a half: Vipul will reach point D.
Now, let's calculate the distances between points.
- OA = 14m (South-East direction)
- AB = 28m (West direction)
- BC = 14m (North-West direction)
- CD = 8m (East direction)
To find the distance between the starting point O and the final point D, we need to find the diagonal distance of the rectangle ABCD.
Using Pythagoras theorem, we can calculate the diagonal distance:
OD² = OA² + AD²
OD² = 14² + 28² + 8²
OD² = 676
OD = √676
OD = 26m
Therefore, the distance between the starting point and the final point is 26m.
But the question asks for the distance of Vipul from the starting point where he stood, which is point O. Therefore, the correct answer is the perpendicular distance from point D to the line joining points OA.
To calculate this distance, we can use the formula:
Distance = (Area of triangle OAD) / (OA)
Using the formula for the area of a triangle, we get:
Area of triangle OAD = (1/2) x AD x OD
Area of triangle OAD = (1/2) x 8 x 26
Area of triangle OAD = 104
Distance = 104 / 14
Distance = 7.43m (approx)
Therefore, the distance of Vipul from the starting point where he stood is approximately 7.43m, which is closest to option A - 20m.
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