Inequality with 4 variables

Algebra Level 5

$\large P=(x+y)(z+t)$

Let $x,y,z,t$ be positive real numbers satisfying $x^2+y^2+z^2+t^2=10$ and $xyzt=4$ .

If the maximum value of the expression is $S$ , find $\lfloor 100 S \rfloor$ .