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In the diagram below, SR = PQ = 20 and RT:TS = 2:5.  Find UV.

 

 Dec 23, 2023
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Triangle PUQ similar to Triangle TUS

 

ST =  (5) / (2 + 5)  * 20  =  100/7

 

So   ST   / QP    =   (100/7) / 20  =  100 /140  =  10/14 =  5/7

 

Therefore altitude of  PUQ  = QV

 And altitude of TUS  =   VR

 

Therefore    VR / QV =  5/7

Therefore     QV   =  (7/12) QR

 

And triangles  QUV and  QSR are similar  

 

Therefore    UV = (7/12)SR =  (7/12) (20)  =  140/12  = 35 / 3   

 

 

cool cool cool

 Dec 23, 2023

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