PIMSO 2025 - Mathematics - Senior Secondary - National Round Question 13

The perimeter of a triangle formed by points A(1,2), B(3,−4), and C(−2,−3) is in the form $x\sqrt{2y}+\sqrt{2z}+\sqrt{2s}$. What is $x+y+z\times s$ if $y<s<z$?