What is the probability that these three pieces can form a triangle?

什么是概率，这三件可以形成一个三角形？
随机将线段分成三个部分.多少的概率，这三件可以形成一个三角形？
设线段（0，a)任意折成三段长分别为x,y,a-x-y,显然有x>0,y>0,a-x-y>0,满足这三个约束条件的(x,y)在平面直角坐标系中的可行域为一个直角三角形，其面积为:(1/2)a^2.
三段长能构成三角形的条件是：任意两边之和大于第三边，也就是：
x+y>a-x-y,a-x-y+x>y,a-x-y+y>x同时成立
即 x+y>a/2,y<a/2,x<a/2同时成立
满足x+y>a/2,y<a/2,x<a/2同时成立的(x,y)在平面直角坐标系中的可行域也为一个直角三角形，其面积为:(1/8)a^2
故此三段能构成三角形的概率为:p=[(1/8)a^2]/[(1/2)a^2]=1/4=0.25

Segment-based (0, a) arbitrary length into three sections, respectively x, y, axy, clearly x> 0, y> 0, axy> 0, satisfy the three constraints (x, y) in the plane at right angles coordinate system of the feasible region of a right triangle, the area of: (1 / 2) a ^ 2.
Three paragraphs long to constitute a condition of the triangle: the sum of any two sides is greater than the third side, that is:
x + y> a-x-y, a-x-y + x> y, a-x-y + y> x at the same time set up
That is, x + y> a / 2, y <a / 2, x <a / 2 a