11. As shown in the figure, square $\mathrm{ABCD}$ and square $\mathbf{EFGH}$ have their four pairs of sides parallel to each other. Connecting $\mathbf{CG}$ and extending it to intersect BD at point $I_{0}$. Given $BD=10, S_{\triangle BFC}=3, S_{\triangle CHD}=5$, then the length of $\mathbf{BI}$ is?
【Answer】 $\frac{15}{4}$
Analysis: Equal area transformation + Connection of the swallow-tail model $\mathrm{BG}, \mathrm{DG}, \mathrm{FG} \| \mathrm{BC}, \mathrm{S}_{\triangle \mathrm{BCG}}=\mathrm{S}_{\triangle \mathrm{BCF}}=3$, similarly, $\mathrm{S}_{\triangle \mathrm{CDG}}=\mathrm{S}_{\triangle \mathrm{CDH}}=5$,
$$
\begin{array}{l}
\mathrm{BI}: \mathrm{DI}=\mathrm{S}_{\triangle \mathrm{BCG}:} \mathrm{S}_{\triangle \mathrm{CDG}}=3: 5, \\
\mathrm{BI}=10 \div(3+5) \times 3=\frac{15}{4}
\end{array}
$$