Answer:
AB = BC = 4

Explanation:
This is a 45-45-90 triangle (right isosceles). This means that the side ratio is
1:1:
, where AC is sqrt 2, and AB and BC are 1. Now, we need to plug this into our ratio. If sqrt 2 is 8, then 1 is x.
8/
= x/1 = x
x = 8/
= 4
(rationalized)
AB and BC are both 4 * sqrt 2