15. Right trapezoid $A B C D$, the upper base is 1, the lower base is 7, connecting point $E$ on side $A B$ and point $F$ on side $D C$, forming a line segment $E F$ parallel to $A D$ and $B C$ that divides the area of the right trapezoid into two equal parts, then the length of line segment $E F$ is $\qquad$
[Answer] 5
[Solution] From the similar model, we know that $\triangle G A D \sim \triangle G B C \Rightarrow \frac{S_{\triangle G A D}}{S_{\triangle G B C}}=\left(\frac{A D}{B C}\right)^{2}=\frac{1}{49}$. Let $S_{\triangle G A D}=k \Rightarrow S_{\triangle G B C}=49 k \Rightarrow S_{A B C D}=48 k$. Since $E F$ divides the area of the right trapezoid into two equal parts, $S_{A E F D}=\frac{1}{2} S_{A B C D}=24 k$, so $S_{\triangle G E F}=S_{\triangle G A D}+S_{A E F D}=25 k$. Since $\triangle G A D \sim \triangle G E F \Rightarrow\left(\frac{A D}{E F}\right)^{2}=\frac{S_{\triangle G A D}}{S_{\triangle G E F}}=\frac{1}{25} \Rightarrow E F=5 A D=5$