2023 AMC 10A Problem 11

A square of area 2 is inscribed in a square of area 3, creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?

\textbf{(A)} \dfrac{1}{5} \qquad \textbf{(B)} \dfrac{1}{4} \qquad \textbf{(C)} 2 - \sqrt{3} \qquad \textbf{(D)} \sqrt{3} - \sqrt{2} \qquad \textbf{(E)} \sqrt{2} - 1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.