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

It's pretty easy not college levlel just some simple high school geomerty.

12

Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.

Because $ST/SR = 2/3$ and $PQ = SR$, 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 $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.