+0

# Geometry help plssss

0
80
2

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

Jul 3, 2020

#1
0

I solved this!  By similar triangles, UV = 10.

Jul 3, 2020
#2
0

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.