[exitwound]

Well, after doing it multiple times (obviously making stupid errors along the way), I think I got it.

A = (s²√3)/4

s= 8/(3^¼)

A'=(√3/4)(2s)(s')

4=(√3/4)(2)[8/(3^¼)](s')
2=(√3/4)(8/(3^¼)](s')
(8/√3)=[8/(3^¼)](s')
(8/(3^¼)) / (8√3) = s'
s' = 3^¼ / 3^ ½ = 3^(-¼)

s' comes out to be 1/(3^¼).