Tia photocopied the image of a design for a monorail track system.

Tia photocopied the image of a design for a monorail track system. The figure below shows the design and its photocopy: 

Two irregular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, BC measures 14 meters. No dimensions on EFGH are shown. 

The ratio of DA : CD is 2 : 3. The total length of track on the design is 46 meters. What is the length, in meters, of side EH on the photocopied image?