ragunandan wrote:
Its still not convincing for me to consider C as the correct answer because no where the question states AB is the third side or the longest side.. If for example we consider the AB = 3 (answer Choice A), The side of the triangle would be 3,6 and 9.. Now 9 becomes the third side and satisfies all the constraints of the third side.. The same is applicable for the rest two choices.. I feel answer in E.. Can someone explain whats the assumption am missing here ?
Hi
ragunandan,
Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?1. It's mentioned in the question statement that AB is the side of triangle ABC. Since we have been given two sides AC and BC, AB has to the third side.
2. Secondly since the question asks the possible length of side AB, we need to consider all possible values of AB i.e. AB can be the shortest side or the longest side of triangle ABC.
3. Lastly AB = 3 is not a legible value of the 3rd side of triangle ABC with the other two sides as AC = 6 and BC = 9. In a triangle the sum of two sides should be greater than the 3rd side. In this case AB + AC = 9 = BC. Similarly AB = 15√3 is also not a legible value. Among the given options AB = 13.5 is the only value for which we can form a triangle with the other two sides being 6 and 9.
Let me know in case you still have any trouble in the explanation
Regards
Harsh