AMC 10 2021-fall-b Problem 15

In square $ABCD$, points $P$ and $Q$ lie on $\overline{AD}$ and $\overline{AB}$, respectively. Segments $\overline{BP}$ and $\overline{CQ}$ intersect at right angles at $R$, with $BR = 6$ and $PR = 7$. What is the area of the square?

$\textbf{(A) }85 \textbf{(B) }93 \textbf{(C) }100 \textbf{(D) }117 \textbf{(E) }125$