I hobbled on my super bad ankle all the way across my basement to get my calculator to do this. Yes, I hauled out the big boy (I have a TI-84 graphing calculator- the thing is beastly).
anyway.
L=.5w (length= half width) A=LW (area=length x width) A=25
simple subsitution
25=LW
25=.5W x W
25=.5W^2
25/.5=W^2
50=W^2 then square root each side (I have no idea how to type that on a computer)
7.07=W
and thus
3.54=L
Hope that helped!