题目内容

(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.

 

【答案】

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

此跷跷板是标准跷跷板,

米,得米.····················································· 5分

若将两端同时都再伸长相同的长度,假设为

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[来源:学。科。网]

使.··································· 9分

························ 11分

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

方案二:如图(4)所示,

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

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

 

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