Quadrilateral PRQS is a trapezoid with bases PQ and RS. The MN median meets the diagonals PR and QS at X and Y, respectively. Find PQ.

jumbean Jun 21, 2024

#1**+1 **

Let the intersection of SQ and PR be point O, the median of SR be A, and the median of XY be B. Then, the ratio of AO to OB is 28:5 (by similar triangles and AA similarity). Next, we know SM=MP, so if C is the median of PQ, then AB to BC is 1:1, so the ratio of AO to OB to BC is 28:5:33. Therefore, the ratio of AO to OC is 28:38 and the length of PQ is 38.

Feel free to tell me if I made a mistake! :D

Tottenham10 Jun 21, 2024

#1**+1 **

Best Answer

Let the intersection of SQ and PR be point O, the median of SR be A, and the median of XY be B. Then, the ratio of AO to OB is 28:5 (by similar triangles and AA similarity). Next, we know SM=MP, so if C is the median of PQ, then AB to BC is 1:1, so the ratio of AO to OB to BC is 28:5:33. Therefore, the ratio of AO to OC is 28:38 and the length of PQ is 38.

Feel free to tell me if I made a mistake! :D

Tottenham10 Jun 21, 2024