As shown in the diagram, PQ is the median of trapezoid ABCD, where AB=25 inches and CD=38 inches. Find XY in inches.
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 vertical 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
base of YOX / base of COD = 6.5 / 38 = 13/76
So XY = (13/76) CD = (13/76) ( 38) = 13 / 2 = 6.5 in