The base PQRS of a cube with each edge of length 2a is horizontal and V is the centre of the face opposite PQRS . Calculate the length(call this PX) of perpendicular from P to VQ .

This is what i did :

I found $\displaystyle VQ=a\sqrt{6}$ , PX will be its half .

$\displaystyle

PV=VQ=a\sqrt{6}

$

$\displaystyle PX=\sqrt{(a\sqrt{6})^2-(\frac{a\sqrt{6}}{2})^2}$

$\displaystyle =\frac{3\sqrt{2}}{2}a $

i got it wrong . where is my mistake ?