- #1
xcrunner448
- 13
- 0
Homework Statement
If a stick is broken at random into 3 pieces, find the probability that the longest of the 3
pieces is at least three times the shortest of the 3 pieces and that the 3 pieces can serve as
the 3 sides of a triangle. Express your answer as a common fraction reduced to lowest
terms.
The Attempt at a Solution
First, I assumed the stick had length 1 to make things easier. The three pieces have length a, b, and c, so a+b+c=1. Also, all three must be less than 0.5 or else you could not make a triangle out of them (if one was >0.5, the sum of the other two would be <0.5). If c is the longest and a is the shortest, then a<=(c/3). From here I am kind of stuck. I have no idea how to go about trying to find the probability.