geometry

This is a repost:  https://web2.0calc.com/questions/trapezoid_21

Hope this helps.

Triangle  AOB  is similar to triangle COD

Then   since  base  CD  =  38/25   of  base   AB,  then the  height  of  COD  = (38/25)  that of  triangle AOB

Then  there are  38 + 25  =    63 equal parts  to  the height of the trapezoid  ...... and 63/2  = 31..5  equal parts on each side of the  midline

And  since the  height of AOB  contains 25  of  these equal parts......then  the height of triangle YOX  must = 31.5  - 25  = 6.5  of the equal parts

And triangles YOX  and COD  are similar

So

base  of  YOX  / base  of  COD     =     6.5  / 38   =    13/76

So  XY  = (13/76) CD  =    (13/76) ( 38) =  13 / 2    =  6.5  in