Problem

2021 Fermat Problem 20

In the diagram, $PRTY$ and $WRSU$ are squares. Point $Q$ is on $PR$ and point $X$ is on $TY$ so that $PQXY$ is a rectangle. Also, point $T$ is on $SU$ , point $W$ is on $QX$ , and point $V$ is the point of intersection of $UW$ and $TY$ , as shown. If the area of rectangle $PQXY$ is $30$ , the length of $ST$ is closest to

$\textbf{(A)}\ 5\quad$ $\textbf{(B)}\ 5.25\quad$ $\textbf{(C)}\ 5.5\quad$ $\textbf{(D)}\ 5.75\quad$ $\textbf{(E)}\ 6$

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

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Category: Fermat
Points: 3
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