Pythagorean theorem:
AC² + BC² = AB²
since this is isosceles (2 sides the same length), we can just let BC = AC and get
AC² + AC² = AB²
2AC² = AB²
AC² = AB²/2
AC = √(AB² / 2)
[tex]\mathrm{AC} = \sqrt{ \left( 6 \sqrt{2} \right)^2 /2} \\ = \sqrt{72/2} = 6[/tex]
AC and BC are 6 meters