Stupid question about straight lines - need help

[runningmarvel]

Hey guys,
I have to do some homework about straight lines. So far I've managed everything without problems, but the I stumpled upon this question:

The perpendicular bisector of the straight line joining the points (3,2) and (5,6) meets the x axis at A and the y axis at B. Prove that the distance AB is equal to 6x"square root 5"(I don't know how to do the symbol...)

I tried to answer this by first finding the gradient of the straight line, then getting the perpendicular gradient of the straight line.
After that I got the midpoint of the straight line and got the equation for the perpendicular line.
From this I found out what A and B were and calculated the distance between them.

The exact numbers I got were:
gradient of straight line=2
gradient of perpendicular line= -0.5
midpoint of straight line= (4,4)
equation for perpendicular line: y=-0.5X+4
A=(8,0) B= (0,4)

The distance between A and B that I got was 4x"square root 5" which means, that I didn't prove this.

What did I get wrong?
Plz help me out, this really annoys me, I've gone through it about 500 times but I just don't see what I did wrong??

Thanks, guys