如图，在长方体上有一只蚂蚁从项点A出发，要爬行到顶点B去找食物，一只长方体的长、宽、高分别为4、1、2
\u5982\u56fe\uff0c\u5728\u957f\u65b9\u4f53\u4e0a\u6709\u4e00\u53ea\u8682\u8681\u4ece\u9879\u70b9A\u51fa\u53d1\uff0c\u8981\u722c\u884c\u5230\u9876\u70b9B\u53bb\u627e\u98df\u7269\uff0c\u4e00\u53ea\u957f\u65b9\u4f53\u7684\u957f\u3001\u5bbd\u3001\u9ad8\u5206\u522b\u4e3a4\u30011\u30012\u89e3\uff1a\u80fd\uff1b\u7ebf\u6bb5AB\u7684\u957f\u5c31\u662f\u8682\u8681\u8d70\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\uff1a\u5982\u56fe1\uff1aAC=4\uff0cBC=2+1=3\uff0c\u2220C=90\u00b0\uff0c\u7531\u52fe\u80a1\u5b9a\u7406\u5f97\uff1aAB=5\uff1b\u5982\u56fe2\uff1aAC=4+1=5\uff0cBC=2\uff0c\u2220C=90\u00b0\uff0c\u5728\u25b3ABC\u4e2d\uff0c\u7531\u52fe\u80a1\u5b9a\u7406\u5f97\uff1aAB=29\uff1e5\uff0c\u2234\u6cbf\u56fe1\u8def\u7ebf\u8d70\u65f6\u6700\u77ed\uff0c\uff1b\u5982\u56fe3\uff1a\u5373\u80fd\u753b\u51fa\u8682\u8681\u8d70\u7684\u6700\u77ed\u8def\u7ebf\uff1a\u5982\u56fe\u4eceA\u5230C\u2032\u518d\u5230B\u6216\u5148\u6cbf\u5e95\u9762\u8d70\u5230C''\u7136\u540e\u8d70\u5230B\uff0e
\u6cbf\u7740A\u81f3B\u4e4b\u95f4\u7684\u76f4\u7ebf\u8ddd\u79bb\u6700\u77ed
\u8ddd\u79bb=[(5+4\uff09^2+3^2]^1/2=(81+9)^1/2=90^1/2\uff0c\u537390\u5f00\u65b9
| 解：线段AB的长就是蚂蚁走的最短距离， 分为两种情况：如图1：AC=4，BC=2+1=3， ∠C=90°，由勾股定理得：AB=5； 如图2：AC=4+1=5，BC=2， ∠C=90°，在△ABC中，由勾股定理得：AB= ＞5， ∴沿图1路线走时最短， 即能画出蚂蚁走的最短路线：如图从A到C再到B． |
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