+0  
 
0
72
1
avatar

A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?

 Apr 1, 2021
 #1
avatar+556 
+1

I like this one. Let the sides be $x,y,1-(x+y)$. By the triangle inequality, all of the following must be true:

$$x<1-x$$

$$y<1-y$$

$$1<2x+2y$$

Graph each of these on the coordinate plane and use the principle of geometric probability. It's $\frac14$. 

 Apr 1, 2021

8 Online Users