Determine the value of a.
https://latex.artofproblemsolving.com/0/9/0/090ba6228af39380edfafa9908b8a3dd14b7a383.png is the picture
It is black not blank
and I know the asymptote([asy]
pair f=(0,sqrt(3)); pair l=(2,sqrt(3)); pair a=(2,0); pair x=(0,0);
pair z=(f+l)/2;
dot(f); dot(l); dot(a); dot(x); dot(z);
draw(x--f--l--a--x--z--a);
draw(rightanglemark(x,f,l,5));
draw(rightanglemark(f,l,a,5));
draw(rightanglemark(l,a,x,5));
draw(rightanglemark(a,x,f,5));
label("$F$",f,NW);
label("$Z$",z,N);
label("$L$",l,NE);
label("$A$",a,SE);
label("$X$",x,SW);
[/asy])
is the asymptote.