一个等腰直角三角形的顶点分别在底边长为4的正三棱柱的三条侧棱上,则...

发布网友发布时间：2024-09-06 01:01

共4个回答

热心网友时间：2024-10-16 14:35

如图，正三棱柱ABC-A1B1C1中，△ABC为正三角形，
边长为4，△DEF为等腰直角三角形，
DF为斜边，设DF长为x，则DE=EF=22x，
作DG⊥BB1，HG⊥CC1，EI⊥CC1，
则EG=DE2?DG2=x22?16，FI=EF2?EI2=x22?16，
FH=FI+HI=FI+EG=2x22?16，
在Rt△DHF中，DF2=DH2+FH2，
即x2=16+（2已赞过已踩过你对这个回答的评价是？评论收起 // 高质or满意or特型or推荐答案打点时间 window.iPerformance && window.iPerformance.mark('c_best', +new Date); F.context('answers')['2370010009'] = {uid:"336525037",imId:"public.1.a1f97a34.3-p6HfkS47voxd7eDdDrQg",passPhoto:"1",id:"2370010009",userName:"逍遥小帝皇",userNameEnc:"%E9%80%8D%E9%81%A5%E5%B0%8F%E5%B8%9D%E7%9A%87",user:{sex:"1",iconType:"6",gradeIndex:"11",grAnswerNum:"835",carefield: [{cid:"1077",cname:"摩尔庄园"},{cid:"1188",cname:"赛尔号"},{cid:"1121",cname:"奥比岛"},{cid:"1220",cname:"弹弹堂"},{cid:"74",cname:"电脑/网络"}],isAuth:"0",authTitle:"",isUserAdmin:"0",userAdminLevel:"",userAdminTitle:"",userAdminType:"",isFamous:"0",isMaster:"0",goodRate:"64"},isAnonymous:"0",isCurrentUser:"0",mapUrl:"",refer:"",replyAskNum:"",threadId:"9480040037",hasComment:"0",qid:"1755004754557226748",raid:"",recommendCanceled:"0"}; F.context('answers')['2370010009']['c_timestamp'] = '1448356664'; F.context('answers')['2370010009'].encodeUid = 'edf64069236f25705e790e14'; F.context('answers')['2370010009'].ext_pack = {"authentic_refuse":"2","authentic_time":"1448356773","display_best_for_se":"1","display_best_for_se_time":"1640796421","dynamic_optime":"1648262440","dynamic_score_detail":"{\"qua_score\":2752,\"time_score\":null,\"ide_score\":null,\"pre_score\":7945}","mode_begintime":"0","mode_qtype":"0","op_uid":"0","reply_entry":"climb_rock"}; F.context('answers')['2370010009'].bit_pack = {"is_recommend":"0","wap_flag":"0","is_pic_contained":"1","media_flag":"0","help_flag":"0","anonymous":"0","is_really_anonymous":"0","level_new":"1","comment_flag":"0","in_mis":"0","auto_recommend":"0","content_rich_flag":"1","prior_flag":"1","hidden_flag":"0","rec_canceled_flag":"0","mis_flag":"0","file_flag":"0","read_flag":"0","is_challenge":"0","ikaudio_flag":"0","mavin_flag":"0","is_delete_lock":"0","authentic_state":"0","is_compulsory_best":"0","dynamic_stick_flag":"0","video_flag":"0","vote_affirmative":"0","vote_negative":"0","is_video":"0","is_baiduyun":"0","is_yike_card":"0","is_baidumap":"0","is_note":"0"}; 逍遥小帝皇
2015-11-24·TA获得超过8.9万个赞知道大有可为答主回答量：8833采纳率：82%帮助的人：723万我也去答题访问个人页关注展开全部

　　分析：由于正三棱柱的底面ABC为等边三角形，可以把一个等腰直角三角形DEF的三个顶点分别在正三棱柱的三条侧棱上，结合图形的对称性可得，该三角形的斜边EF上的中线DG的长等于底面三角形的高，从而得出等腰直角三角形DEF的中线长，最后得到该三角形的斜边长即可。
解答：
解：一个等腰直角三角形DEF的三个顶点分别在正三棱柱的三条侧棱上，∠EDF=90°，已知正三棱柱的底面边长为AB=2，则该三角形的斜边EF上的中线DG=根号。
∴斜边EF的长为2倍的根号3。
故答案为：2倍的根号3。

　　如图，正三棱柱ABC-A1B1C1中，△ABC为正三角形，
边长为4，△DEF为等腰直角三角形，
DF为斜边，设DF长为x，则DE=EF=22 x，作DG⊥BB1，HG⊥CC1，EI⊥CC1，则EG=

　　DE2−DG2=2 ，FI=EF2−EI2 =x2 2 −16 ，

　　FH=FI+HI=FI+EG=2x2 2 −16 ，在Rt△DHF中，DF2=DH2+FH2，即x2=16+2。

已赞过已踩过你对这个回答的评价是？评论收起 F.context('answers')['2367172915'] = {uid:"815845723",imId:"public.1.46cead87.lav5gBUnWLd_32ea7EV91A",passPhoto:"1",id:"2367172915",userName:"飞翔雨儿3",userNameEnc:"%E9%A3%9E%E7%BF%94%E9%9B%A8%E5%84%BF3",user:{sex:"1",iconType:"6",gradeIndex:"14",grAnswerNum:"1919",carefield: [{cid:"83",cname:"教育/科学"},{cid:"983",cname:"数学"}],isAuth:"0",authTitle:"",isUserAdmin:"0",userAdminLevel:"3",userAdminTitle:"初级芝麻将",userAdminType:"1",isFamous:"0",isMaster:"0",goodRate:"64"},isAnonymous:"0",isCurrentUser:"0",mapUrl:"",refer:"",replyAskNum:"",threadId:"9468691661",hasComment:"0",qid:"1755004754557226748",raid:"",recommendCanceled:"0"}; F.context('answers')['2367172915']['c_timestamp'] = '1448081692'; F.context('answers')['2367172915'].encodeUid = '5bd14069236f25705e79a030'; F.context('answers')['2367172915'].ext_pack = {"anony_good_value":"1","authentic_refuse":"2","authentic_time":"1448081659","dynamic_optime":"1648262440","dynamic_score_detail":"{\"qua_score\":2480,\"time_score\":null,\"ide_score\":null,\"pre_score\":7738}","mode_begintime":"0","mode_qtype":"0","op_uid":"0","reply_entry":"team"}; F.context('answers')['2367172915'].bit_pack = {"is_recommend":"0","wap_flag":"0","is_pic_contained":"0","media_flag":"0","help_flag":"0","anonymous":"0","is_really_anonymous":"0","level_new":"1","comment_flag":"0","in_mis":"0","auto_recommend":"0","content_rich_flag":"0","prior_flag":"1","hidden_flag":"0","rec_canceled_flag":"0","mis_flag":"0","file_flag":"0","read_flag":"0","is_challenge":"0","ikaudio_flag":"0","mavin_flag":"0","is_delete_lock":"0","authentic_state":"0","is_compulsory_best":"0","dynamic_stick_flag":"0","video_flag":"0","vote_affirmative":"0","vote_negative":"0","is_video":"0","is_baiduyun":"0","is_yike_card":"0","is_baidumap":"0","is_note":"0"}; 飞翔雨儿3
2015-11-21·TA获得超过4万个赞知道大有可为答主回答量：5117采纳率：70%帮助的人：1100万我也去答题访问个人页关注展开全部分析：由于正三棱柱的底面ABC为等边三角形，可以把一个等腰直角三角形DEF的三个顶点分别在正三棱柱的三条侧棱上，结合图形的对称性可得，该三角形的斜边EF上的中线DG的长等于底面三角形的高，从而得出等腰直角三角形DEF的中线长，最后得到该三角形的斜边长即可。
解答：
解：一个等腰直角三角形DEF的三个顶点分别在正三棱柱的三条侧棱上，∠EDF=90°，已知正三棱柱的底面边长为AB=2，则该三角形的斜边EF上的中线DG=根号。
∴斜边EF的长为2倍的根号3。
故答案为：2倍的根号3.已赞过已踩过你对这个回答的评价是？评论收起 F.context('answers')['2174913895'] = {uid:"612213664",imId:"public.1.68da6338.jTZtW-vIf0C3dlC7eFLIqA",id:"2174913895",userName:"北斗流岚_北斗",userNameEnc:"%E5%8C%97%E6%96%97%E6%B5%81%E5%B2%9A_%E5%8C%97%E6%96%97",user:{sex:"1",iconType:"6",gradeIndex:"4",grAnswerNum:"6",carefield: [{cid:"1186",cname:"QQ宠物"}],isAuth:"0",authTitle:"",isUserAdmin:"0",userAdminLevel:"",userAdminTitle:"",userAdminType:"",isFamous:"0",isMaster:"0",goodRate:"30"},isAnonymous:"0",isCurrentUser:"0",mapUrl:"",refer:"",replyAskNum:"",threadId:"8699655581",hasComment:"0",qid:"1755004754557226748",raid:"",recommendCanceled:"0"}; F.context('answers')['2174913895']['c_timestamp'] = '1429283901'; F.context('answers')['2174913895'].encodeUid = 'a0a34069236f25705e797d24'; F.context('answers')['2174913895'].ext_pack = {"dynamic_optime":"1648262440","dynamic_score_detail":"{\"qua_score\":1095,\"time_score\":null,\"ide_score\":null,\"pre_score\":2997}","ignore_spam":"1","mode_begintime":"0","mode_qtype":"0","op_uid":"0","reason_1_2":"1","reply_entry":"qb_wise_search","submit_from":"iphone"}; F.context('answers')['2174913895'].bit_pack = {"is_recommend":"0","wap_flag":"1","is_pic_contained":"0","media_flag":"0","help_flag":"0","anonymous":"0","is_really_anonymous":"0","level_new":"1","comment_flag":"0","in_mis":"0","auto_recommend":"0","content_rich_flag":"0","prior_flag":"0","hidden_flag":"0","rec_canceled_flag":"0","mis_flag":"0","file_flag":"0","read_flag":"0","is_challenge":"0","ikaudio_flag":"0","mavin_flag":"0","is_delete_lock":"0","authentic_state":"0","is_compulsory_best":"0","dynamic_stick_flag":"0","video_flag":"0","vote_affirmative":"0","vote_negative":"0","is_video":"0","is_baiduyun":"0","is_yike_card":"0","is_baidumap":"0","is_note":"0"}; 北斗流岚_北斗
2015-04-17·TA获得超过253个赞知道答主回答量：59采纳率：0%帮助的人：18.4万我也去答题访问个人页关注展开全部4根3已赞过已踩过你对这个回答的评价是？评论收起收起更多回答（2）推荐律师服务：若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询其他类似问题2015-02-10一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上．已知...32015-02-06一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上．已知...2011-03-11『急』一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上...32011-03-27『急』一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上...2012-07-28等腰直角三角形顶角的顶点在数对(3,4),202012-04-18一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上，已知...42012-08-19一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上。已知...132011-03-14『急』一个等腰直角三角形的三个顶点分别在正三棱柱的三条侧棱上...6更多类似问题 >为你推荐：特别推荐“网络厕所”会造成什么影响？华强北的二手手机是否靠谱？新生报道需要注意什么？癌症的治疗费用为何越来越高？百度律临—免费法律服务推荐超3w专业律师，24H在线服务，平均3分钟回复免费预约随时在线律师指导专业律师一对一沟通完美完成等你来答换一换帮助更多人下载百度知道APP，抢鲜体验使用百度知道APP，立即抢鲜体验。你的手机镜头里或许有别人想知道的答案。扫描二维码下载×个人、企业类侵权投诉违法有害信息,请在下方选择后提交

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热心网友时间：2024-10-16 14:28

　　如图，正三棱柱ABC-A1B1C1中，△ABC为正三角形，
边长为4，△DEF为等腰直角三角形，
DF为斜边，设DF长为x，则DE=EF=22 x，作DG⊥BB1，HG⊥CC1，EI⊥CC1，则EG=

　　DE2−DG2=2 ，FI=EF2−EI2 =x2 2 −16 ，

　　FH=FI+HI=FI+EG=2x2 2 −16 ，在Rt△DHF中，DF2=DH2+FH2，即x2=16+2。

热心网友时间：2024-10-16 14:29

热心网友时间：2024-10-16 14:30

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