tag:blogger.com,1999:blog-3550204829234352390.post2446684405968059258..comments2024-03-27T09:13:48.546+08:00Comments on 研發養成所 ( Bridan's Blog - 4rdp, For R&D Person ): 訓練數學感 140 ─ 內接正方形有多大Bridanhttp://www.blogger.com/profile/17055047757114667099noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3550204829234352390.post-8972490959694640402017-06-28T08:42:25.436+08:002017-06-28T08:42:25.436+08:00正解,這題小朋友考試當時未解出,TMT採用填選題是填充題的變體,算出答案後用2B鉛筆把數值塗到答案卡...正解,這題小朋友考試當時未解出,TMT採用填選題是填充題的變體,算出答案後用2B鉛筆把數值塗到答案卡上。30題約一小時解答,滿分150,他說大多數同學沒有超過100分。西瓜若參加應該輕鬆得高分。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-37703550350770001122017-06-27T23:42:05.406+08:002017-06-27T23:42:05.406+08:00(1)
連DF,CE⇒DF=AD=BC=CE=10
(2)
在△DFG和△CEH中:
∵DF=CE(...(1)<br />連DF,CE⇒DF=AD=BC=CE=10<br />(2)<br />在△DFG和△CEH中:<br />∵DF=CE(已證),HE=GF(正方形EHGF邊長),∠FGD=∠FGH=90°=∠EHG=∠EHC(正方形EHGF內角)<br />∴△DFG≌△CEH(RHS全等)<br />(3)<br />∵△DFG≌△CEH<br />∴DG=CH(對應邊等長)<br />⇒DH=DG-HG=CH-HG=CG<br />(4)令正方形EHGF邊長2a<br />⇒DH=CG=(1/2)(10-2a)=5-a<br />⇒DG=10-CG=10-(5-a)=a+5<br />(4)在△DFG中:<br />∵∠DGF=∠HGF=90°(正方形EHGF內角)<br />∴DG²+GF²=DF²(畢氏定理)<br />⇒(a+5)²+(2a)²=10²<br />⇒5a²+10a-75=0<br />⇒a²+2a-15=0<br />⇒a=3V-5 (負不合)<br />帶入原假設,得正方形EFGH邊長=2a=6(cm)<br /><br />解題結束。<br /><br />誠實來說,一開始根本沒有人會想去證明DH=CG,而是靠感覺認為直接是相等的。我也是一樣,哈哈。<br />如果是非選題的話,DH=CG的證明就顯得有必要性,否則應該會扣分。<br /><br /><br /><br />.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-89872253225026862512017-06-27T20:55:45.312+08:002017-06-27T20:55:45.312+08:00答案對,解題過程留給高手補充。答案對,解題過程留給高手補充。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-58625944320472258582017-06-27T19:12:47.259+08:002017-06-27T19:12:47.259+08:00正方形邊長=6,周長=24.
使用簡單代數及畢氏定理解題。正方形邊長=6,周長=24.<br />使用簡單代數及畢氏定理解題。行天下https://www.blogger.com/profile/04992727596324526135noreply@blogger.com