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.

Answer: 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 $UV = (3/5) SR = / boxed{12}$.