Task 667
Task 667: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction? asy…
The task
In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction? [asy] draw((0,0)--(1,0)--(.4,.5)--cycle); label("$A$",(.4,.5),N); label("$B$",(1,0),SE); label("$C$",(0,0),SW); label("$x+9$",(.5,0),S); label("$x+4$",(.7,.25),NE); label("$3x$",(.2,.25),NW); [/asy]