22. When proving the Pythagorean theorem, four congruent right triangles can be used to form a square (as shown in Figure 1), and we call such a figure a "string figure."
A similar method of constructing string figures is often used in rectangles. As shown in Figure 2, draw a line $EF$ through vertex $A$ of rectangle $ABCD$, and draw perpendiculars from points $B$ and $D$ to $EF$, with the feet of the perpendiculars being points $E$ and $F$, respectively, then $\triangle BEA \sim \triangle AFD$.
As shown in Figure 3, in rectangle $ABCD$, $AD=5$, $AB=10$, construct congruent right triangles $ADE$ and $CBF$ with $AD$ and $BC$ as the hypotenuses, respectively. If $AE=CF=3$, then $EF^{2}=$ . $\qquad$
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