Equilateral triangles 3

Assume a point $D$ inside an equilateral triangle $ABC$ of side length $t$ and with $AD=x$, $BD=y$, $CD=z$, $0<x\le y\le z$, which is represented as quadruple $(x,y,z,t)$.

If $x,y,z,t$ are all integers and they are coprime, the quadruple $(x,y,z,t)$ is called primitive integer solution. For example, $(57,65,73,112)$ is such a solution. And it’s known that there are infinitely many solutions of primitive integer quadruple $(x,y,z,t)$.

Find all such solutions for $t\le 5000$.

Answer format: [number of solutions],[sum of $x+y+z+t$ of all solutions]

Example: 3,1237 for $t\le 200$
(explanation: there are total 3 solutions $(57,65,73,112)$, $(73,88,95,147)$, $(43,147,152,185)$)