IMAS 2021–2022 Junior Division, Round 2 Question 15

It is known that positive numbers $x,y,z$ satisfy $\begin{cases}x^2+xy+y^2=5^2,\\y^2+yz+z^2=12^2,\\z^2+xz+x^2=13^2.\end{cases}$ What is the value of $(x+y+z)^2$?