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In the diagram below, RT:TS = 1:2 and SR = PQ = 20. Find UV.

 Jul 3, 2020
 #1
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I solved this!  By similar triangles, UV = 10.

 Jul 3, 2020
 #2
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That's actually wrong. I know this because I just solved it.

 

Because PQ, UV, and  SR are all perpendicular to QR, we have .PQ || UV || SR Therefore, we have
Because ST/SR = 2/3 and PQ = SR, we have
Since , we have .

We have  by AA Similarity, so . Therefore, we have:

 

\(\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\)


Since UQ/US = 3/2, we have UQ/QS = 3/5.

We have triangle UQV ~ trinagle SQR by AA Similarity, so UV/SR = UQ/QS = 3/5.

 

Please check your answers more carefully. I have heard of some trolls on this site that only write a one sentance answer with the wrong answer like, "By similar triangles, 19". I would highly recommend people doubting people who answer questions in that way and check if their answer does, indeed, work. For anyone to believe you, please write down a specific step by step answer, so people can see your work. Although this might just be a mistake in your calculations, I want to put that out there. If people are just randomly trolling, it is a shame, really. Thank you.

Guest Jul 3, 2020
edited by Guest  Jul 3, 2020
edited by Guest  Jul 3, 2020

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