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[來源:學。科。網]
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