Questions: What is DE? DE = □

Solution Steps

Triangles $\triangle FGE$ and $\triangle DGE$ are congruent because: \begin{itemize} \item $FG = DG = 41$ \item $\angle FGE = \angle DGE = 90^\circ$ \item $GE$ is a common side \end{itemize} By Side-Angle-Side (SAS) criterion, $\triangle FGE \cong \triangle DGE$.

Since $\triangle FGE \cong \triangle DGE$, their corresponding sides are equal. Thus, $FE = DE$. We are given that $FE = 2s$. Therefore, $DE = 2s$.

We are given that $DE = s + 23$. Since $DE = 2s$, we can write $2s = s + 23$. Subtracting $s$ from both sides gives $s = 23$.

We know that $DE = 2s$ and $s = 23$. Therefore, $DE = 2 \times 23 = 46$.

Final Answer The final answer is $\boxed{46}$