Consider the triangle ABX.
Determine the length of AX by using the pythagoras theorem.
The length of XY is twice of side AX. So XY = 36
Consider trinagle XYZ.
Detertmine the length of side YZ by using pythagoras theorem.
The length of side YC is half of YZ so YC = 24.
Determine the length of side AC by using pyhtagras theorem in triangle AYC.
So length of AC is 30.
Answer: 30