解：設(shè)矩形的邊長(zhǎng)為?$x\mathrm {cm}$?
?$ ①$?當(dāng)?$5\ \mathrm {cm} $?為等腰三角形的腰時(shí)
?$ x(9-x)=\frac 12×8×3$?
?$ $?解得?$x_{1}=\frac {9+\sqrt {33}}2，$??$x_{2}=\frac {9-\sqrt {33}}2$?
經(jīng)檢驗(yàn)，兩根均符合題意
?$②$?當(dāng)?$5\ \mathrm {cm} $?為等腰三角形的底時(shí)
?$ x(9-x)=\frac 12×5×6$?
?$ $?解得?$x_{1}=\frac {9+\sqrt {21}}2，$??$x_{2}=\frac {9-\sqrt {21}}2$?
經(jīng)檢驗(yàn)，兩根均符合題意
∴矩形的長(zhǎng)為?$ \frac {9+\sqrt {33}}2、$??$\frac {9-\sqrt {33}}2、$??$\frac {9+\sqrt {21}}2、$??$\frac {9-\sqrt {21}}2$?
