Problem

2014 Fermat Problem 20

In the diagram, $\triangle PQR$ has $PQ = QR = RP = 30$ . Points $S$ and $T$ are on $PQ$ and $PR$ , respectively, so that $ST$ is parallel to $QR$ . Points $V$ and $U$ are on $QR$ so that $TU$ is parallel to $PQ$ and $SV$ is parallel to $PR$ . If $VS + ST + TU = 35$ , the length of $VU$ is

$\textbf{(A)}\ 21\quad$ $\textbf{(B)}\ 15\quad$ $\textbf{(C)}\ 18\quad$ $\textbf{(D)}\ 20\quad$ $\textbf{(E)}\ 25$

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.

Show/Hide Problem Tags

Problem Tags: No tags

Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)

Problem feedback

Difficulty —

Category: Fermat
Points: 3
Back to practice
Train more like this