A, B, C, D and E are five friends standing in a park. The distance between A and C and that of B and C are same. E and C are 45m apart in west-east direction. A is towards west of C at a distance of 25m from E. C is in between B and D and in north direction wrt B.Q.If the distance between B and D is 35m, then calculate the distance between A and D.a)15b)20c)25d)30Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Understanding the Scenario
Let's visualize the arrangement of friends A, B, C, D, and E based on the given information.

Positioning of Friends
- **C's Position**: Place C at the origin (0,0).
- **E's Position**: E is 45m east of C, so E is at (45,0).
- **A's Position**: A is 25m west of E, which places A at (20,0).
Now we have:
- A (20,0)
- C (0,0)
- E (45,0)

Positions of B and D
- **B's Position**: C is north of B, and since the distance between A and C equals the distance between B and C, the distance is 25m. Therefore, B is at (0,-25).
- **D's Position**: Since B is south of C and the distance between B and D is 35m, D must be 35m north of B. Thus, D is at (0,10).
Now we have:
- B (0,-25)
- D (0,10)

Calculating Distance between A and D
To find the distance between A and D, we can use the distance formula:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$
Substituting A (20,0) and D (0,10):
$$
\text{Distance} = \sqrt{(0 - 20)^2 + (10 - 0)^2} = \sqrt{400 + 100} = \sqrt{500} \approx 25
$$

Conclusion
Thus, the distance between A and D is approximately 25m, making the correct answer option 'C'.

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