2014_QNR 16. Two men, starting at the same point, walk in opposite directions for 12 metres, turn to their left and walk another 5 metres. What is the distance between them now?
1. 26 metres
2. 13 metres
3. 24 metres
4. 34 metres
Ans: Let us draw the figure for this:
Person, P1 and P2 start from point O and after walking for 12 meters reach points B and C respectively. Both take left and walk for another 5 meters to reach A and D respectively. We need to find AD.
Both, triangle OAB and OCD are right angled triangle and OA and OD are the respective hypotenuse. Using Pythagoras theorem, OA = √( OC² + CD²) = √(12²+ 5²) = 13 = OD. Therefore, AD= 26. Option 1.
Another way of solving:
Although this question is easy to solve using the above method, let us look through a different prism.
The property we are gonna use is “Hypotenuse is the largest side in a right angled triangle“.
OA being a hypotenuse should be the largest side; it should be greater than 12. Similarly, OD > 12. Thus, AD > 24. We can reject out options 2 and 3.
Also, The property we are gonna use is “Sum of any two sides of a triangle is greater than the third side“.
OB + BA > OA
=> OA < 17
Similarly, OD < 17. AD = OA + OD < 34. We can reject out option 4.