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As shown in the diagram, PQ is the median of trapezoid ABCD where AB = 25 inches and CD = 30 inches. Find XY in inches.

 

 Feb 12, 2021
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Triangle  AOB  is similar to triangle COD

 

Then   since  base  CD  =  6/5   of  base   AB,  then the  height  of  COD  = (6/5)  that of  triangle AOB

 

Then  there  11 equal parts  to  the height of the trapezoid  ...... and 11/2  = 5.5  equal parts on each side of the  midline

 

And  since the  height of AOB  contains 5  of  these......then  the height of triangle YOX  must = .5  of these

 

And triangles YOX  and COD  are similar

 

So

 

base  of  YOX  / base  of  COD     =   .5  / 6  =   1/12

 

So  XY  =(1/12) CD  =   30 / 12  =  5/2  in  =    2.5  in 

 

 

cool cool cool

 Feb 12, 2021
edited by CPhill  Feb 20, 2021

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