一根绳子,随机截成3段,可以组成一个三角形的概率有多大

“`” 参考回答：

设绳子长为a,折成三段的长度为x,y,a-x-y从而得到<img alt=""img"" referrerpolicy=""no-referrer"" src=""https://uploadfiles.nowcoder.com/images/20190315/311436_1552619963669_064E526A1DA18550FFB74E4784F64063"">,满足这三个约束条件在平面直角坐标系中的可行域为一个直角三角形,面积为<img alt=""img"" referrerpolicy=""no-referrer"" src=""https://uploadfiles.nowcoder.com/images/20190315/311436_1552619943001_8A48005923F53BEF73810EE96C8BAD55"">。而构成三角形的条件,任意两边和大于第三边的条件x+y>a-x-y,a-y>y,a-x>x同时成立。满足以上不等式在平面直角坐标系中也是一个直角三角形,面积为<img alt=""img"" referrerpolicy=""no-referrer"" src=""https://uploadfiles.nowcoder.com/images/20190315/311436_1552619917275_8618A0DDC281681A765A13B5B312BC65"">,所以构成三角形概率为<img alt=""img"" referrerpolicy=""no-referrer"" src=""https://uploadfiles.nowcoder.com/images/20190315/311436_1552619894762_ADC5BAECF47FE96BB75189644F13DAD1"">

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