help me. thank you

The length of $AB$ & $BC$ are 6. This is because the hypotenuse of a right-isosceles triangle is $\frac{h}{\sqrt{2}}.$

From this, you know that $AB\Xi BC$ and the values are $\frac{6\sqrt{2}}{\sqrt{2}} = 6.$

If AB is 6, then 6 is the side of a 30-60-90 triangle or a half-cut equilateral triangle. This would mean that x is half of 6 or x is 3.

I had to write my answer in multiple posts since LaTeX hates me right now. I might be wrong so make sure to double check my work. Good Luck!

Your very much welcome!

$AB=BC \qquad\text{ABC is a right angled isosceles triangle}\\ 2*(AB)^2=(6\sqrt2)^2\\ 2*(AB)^2=72\\ (AB)^2=36\\ AB=BC=6$

$cos 60=\frac{1}{2}$

$\frac{x}{6}=\frac{1}{2}\\ x=3$

Or you can write it in 1 post, good thinking!