What is the value of x in the diagram?

The altitude of the triangle = 8 * √3/2 = 4√3  = √48

The triangle on the right is a 45-45-90 right triangle

Both  legs  = the altitude

The hypotenuse, x  =  √  [ (√48)^2 + (√48)^2 ]   = √ [48 + 48 ] = √96  = √ [16 * 6 ] = 4√6