Question

（本小題滿分12分）

小胖和小瘦去公園玩標準的蹺蹺板游戲，兩同學越玩越開心，小胖對小瘦說：“真可惜！

我只能將你最高翹到1米高，如果我倆各邊的蹺蹺板都再伸長相同的一段長度，那么我

就能翹到1米25，甚至更高！”

（1）你認為小胖的話對嗎？請你作圖分析說明；

（2）你能否找出將小瘦翹到1米25高的方法？試說明．

 

Answer 1

解：（1）小胖的話不對．·································· 2分

小胖說“真可惜！我現在只能將你最高翹到1米高”，情形如圖（1）所示，

是標準蹺蹺板支架的高度，是蹺蹺板一端能翹到的最高高度1米，是地面．

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

又此蹺蹺板是標準蹺蹺板，，

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

若將兩端同時都再伸長相同的長度，假設為米．

如圖（2）所示，

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

，即．

，同理可得．

，由米，得米．············ 7分

綜上所述，蹺蹺板兩邊同時都再伸長相同的一段長度，蹺蹺板能翹到的最高高度始終為支架高度的兩倍，所以不可能翹得更高．

（2）方案一：如圖（3）所示，

保持長度不變．將

延長一半至，即只將小瘦一邊伸長一半． 8分

使則．··································· 9分

由得························ 11分

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

方案二：如圖（4）所示，

只將支架升高0.125米．········································ 8分

又米．···························· 9分

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

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

（注：其它方案正確，可參照上述方案評分！）

解析:略