7 cm long stick cut three pieces. length of each pieces is natural number what is the probability of forming triangle from the three pieces of sticks?
answer 1/4 but i have step by step answer this question
Answers
Answer:
Step-by-step explanation:
The triangle inequality helps us show that if any of the lengths is greater than the half of the length of the rod, a triangle can not be formed. There are 3 outcomes like that; either the first or the second or the third part can be larger than half of the length of the rod.
The other possibility is that none of the lengths are larger than the half of the length of the rod. Again using the triangle inequality, we can show that this is the necessary and sufficient condition to form a triangle. So, we have a total of 4 possible outcomes.
Each point on the rod is equally likely to be cut while breaking the rod into three parts. Thus, all these 4 possible outcomes mentioned above are equally likely to occur. Then, the probability to form a triangle out of these three parts is simply:
Probability = # of outcomes forming a triangle / # of total outcomes = 1/4 = 25%
I have posted my solution here: Probability to form a Triangle by breaking a Rod