Question

（本小題滿分12分）
小胖和小瘦去公園玩標(biāo)準(zhǔn)的蹺蹺板游戲，兩同學(xué)越玩越開(kāi)心，小胖對(duì)小瘦說(shuō)：“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(zhǎng)相同的一段長(zhǎng)度，那么我
就能翹到1米25，甚至更高！”
（1）你認(rèn)為小胖的話對(duì)嗎？請(qǐng)你作圖分析說(shuō)明；
（2）你能否找出將小瘦翹到1米25高的方法？試說(shuō)明．

Answer 1

解：（1）小胖的話不對(duì)．······················ 2分
小胖說(shuō)“真可惜！我現(xiàn)在只能將你最高翹到1米高”，情形如圖（1）所示，

是標(biāo)準(zhǔn)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(biāo)準(zhǔn)蹺蹺板，，
而米，得米．····················································· 5分
若將兩端同時(shí)都再伸長(zhǎng)相同的長(zhǎng)度，假設(shè)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(shí)都再伸長(zhǎng)相同的一段長(zhǎng)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(zhǎng)度不變．將
延長(zhǎng)一半至，即只將小瘦一邊伸長(zhǎng)一半． 8分[來(lái)源:學(xué)。科。網(wǎng)]
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(píng)分！）

解析