Question

（本小题满分12分）

小胖和小瘦去公园玩标准的跷跷板游戏，两同学越玩越开心，小胖对小瘦说：“真可惜！

我只能将你最高翘到1米高，如果我俩各边的跷跷板都再伸长相同的一段长度，那么我

就能翘到1米25，甚至更高！”

（1）你认为小胖的话对吗？请你作图分析说明；

（2）你能否找出将小瘦翘到1米25高的方法？试说明．

 

Answer 1

解：（1）小胖的话不对．·································· 2分

小胖说“真可惜！我现在只能将你最高翘到1米高”，情形如图（1）所示，

是标准跷跷板支架的高度，是跷跷板一端能翘到的最高高度1米，是地面．

························································································· 4分

又此跷跷板是标准跷跷板，，

而米，得米．····················································· 5分

若将两端同时都再伸长相同的长度，假设为米．

如图（2）所示，

米，米········································· 6分

，即．

，同理可得．

，由米，得米．············ 7分

综上所述，跷跷板两边同时都再伸长相同的一段长度，跷跷板能翘到的最高高度始终为支架高度的两倍，所以不可能翘得更高．

（2）方案一：如图（3）所示，

保持长度不变．将

延长一半至，即只将小瘦一边伸长一半． 8分

使则．··································· 9分

由得························ 11分

米．··············································· 12分

方案二：如图（4）所示，

只将支架升高0.125米．········································ 8分

又米．···························· 9分

．··················································································· 11分

米．·················································································· 12分

（注：其它方案正确，可参照上述方案评分！）

解析:略