A cylinder of base radius 4cm is opened at one end . If the ratio of the area of it's base to that of it's curved surface area is 1:4, Calculate the height of the cylinder

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?