After using similarity rule im stuck as i cant find segment CF.

[jagged copper]

We can apply cos rule on angle DEC, because we know all the sides of triangle DEC. Then we get cos=5/12

That means sin= √119/12

So in triangle def, ef/de= sin =√119/12

So x will come out to be some irrational. But I'm not sure if my calculations were correct, so please recheck

[vernal pike]

We dont know DE though

[jagged copper]

Triangle ABC is iscosceles and triangle DEC is similiar to abc

[vernal pike]

so 6

[jagged copper]

So DE=DC=6

[vernal pike]

ohh okay

well thanks