We have
[tex]T=\sqrt{F_x^2+F_y^2+F_z^2}[/tex]
And we know that
[tex]T=15,\quad F_z=F_x,\quad F_x=2F_y[/tex]
So, we can actually express the variables in term of numbers and [tex]F_y[/tex] alone:
[tex](T,F_x,F_y,F_z)=(15, 2F_y,F_y,2F_y)[/tex]
And the expression becomes
[tex]15=\sqrt{(2F_y)^2+(F_y)^2+(2F_y)^2} \iff 15=\sqrt{9F_y^2}=3F_y[/tex]
And dividing both sides by 3 we get
[tex]3F_y=15 \iff F_y=5[/tex]
And since [tex]F_z=2F_y[/tex], we have [tex]F_z=10[/tex]
