解析:
按边长组合分类:
1. 等边三角形:(4,4,4),(7,7,7),(8,8,8),(12,12,12),共4种;
2. 等腰三角形:
腰4cm:(4,4,7),(4,4,8),共2种;
腰7cm:(7,7,4),(7,7,8),(7,7,12),共3种;
腰8cm:(8,8,4),(8,8,7),(8,8,12),共3种;
腰12cm:(12,12,4),(12,12,7),(12,12,8),共3种;
3. 不等边三角形:(4,7,8),(7,8,12),(4,8,12)(舍),共2种;
总围法:4+2+3+3+3+2=17
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