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Directions for Questions use the following information and answer the following questions: ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.
Then D is
  • a)
    3 km east and 1 km north of A
  • b)
    3 km east and √3 km north of A
  • c)
    √3 km east and 1 km south of A
  • d)
    √3 km west and 3 km north of A
  • e)
    Inadequate data
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Directions for Questions use the following information and answer the...
Based on the data given, we can draw the following figure
In triangle BDN,
BD2 = BN2 + DN2
4 = 1 + DN2
Hence, DN = √3
Hence, option 2 is correct
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Most Upvoted Answer
Directions for Questions use the following information and answer the...
Explanation:

Given:
- ABC forms an equilateral triangle in which B is 2 km from A.
- A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C.
- He, then, reverses direction and walks till he reaches a point E directly south of C.

To find:
- The location of point D.

Solution:
- Let's draw the equilateral triangle ABC and the path of the person as shown below:

![image.png](attachment:image.png)

- As per the given information, triangle ABC is equilateral and B is 2 km from A. This means that AB = AC = BC = 2 km.
- The person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. This means that BD is parallel to AC and DC is perpendicular to AC.
- Let's assume that the distance BD is x km. Then, CD will also be x km as DC is perpendicular to AC and AC is 2 km (as per the given information). Therefore, BD = CD = x km.
- Also, as BD is parallel to AC, angle BDC = angle C. Since triangle ABC is equilateral, angle C = 60 degrees. Therefore, angle BDC = 60 degrees.
- Let's now apply trigonometry to find the distance between D and A:
- In triangle ABD, angle ADB = 120 degrees (as angle BDC = 60 degrees)
- Using the cosine rule, we get:

AB^2 + BD^2 - 2*AB*BD*cos(120) = AD^2

2^2 + x^2 + 2*2*x*(-0.5) = AD^2

AD^2 = x^2 - 4x + 4 + 4

AD^2 = x^2 - 4x + 8

AD^2 = (x - 2)^2 + 4

AD = sqrt((x - 2)^2 + 4)

- Therefore, the distance between D and A is sqrt((x - 2)^2 + 4) km.
- Now, the person reverses direction and walks till he reaches a point E directly south of C. This means that CE is parallel to BD and DE is perpendicular to BD.
- Let's assume that the distance CE is y km. Then, BE will also be y km as BE is parallel to AC and AC is 2 km (as per the given information). Therefore, CE = BE = y km.
- Also, as CE is parallel to BD, angle CED = angle B. Since triangle ABC is equilateral, angle B = 60 degrees. Therefore, angle CED = 60 degrees.
- Let's now apply trigonometry to find the distance between E and A:
- In triangle ACD, angle ACD = 120 degrees (as angle CED = 60 degrees)
- Using the cosine rule, we get:

AC^2 + CD^2 - 2*AC*CD*cos(120) = AD^2

2^2 + x^2 - 2*2*x*(-0.5
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Directions for Questions use the following information and answer the following questions: ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa) 3 km east and 1 km north of Ab) 3 km east and √3 km north of Ac) √3 km east and 1 km south of Ad) √3 km west and 3 km north of Ae) Inadequate dataCorrect answer is option 'B'. Can you explain this answer?
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Directions for Questions use the following information and answer the following questions: ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa) 3 km east and 1 km north of Ab) 3 km east and √3 km north of Ac) √3 km east and 1 km south of Ad) √3 km west and 3 km north of Ae) Inadequate dataCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Questions use the following information and answer the following questions: ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa) 3 km east and 1 km north of Ab) 3 km east and √3 km north of Ac) √3 km east and 1 km south of Ad) √3 km west and 3 km north of Ae) Inadequate dataCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Questions use the following information and answer the following questions: ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C.Then D isa) 3 km east and 1 km north of Ab) 3 km east and √3 km north of Ac) √3 km east and 1 km south of Ad) √3 km west and 3 km north of Ae) Inadequate dataCorrect answer is option 'B'. Can you explain this answer?.
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