题目内容
一只蚂蚁从长为4cm、宽为3cm,高是5cm的长方体纸箱的A点沿纸箱爬到B点,那么它所行的最短路线的长是________cm.
![](http://thumb.1010pic.com/pic5/latex/104679.png)
分析:先将图形展开,再根据两点之间线段最短,再由勾股定理求解即可.
解答:
![](http://thumb.1010pic.com/pic5/upload/201304/51d65590d4534.png)
解:将长方体展开,如图1所示,连接A、B,根据两点之间线段最短,AB=
![](http://thumb.1010pic.com/pic5/latex/209407.png)
![](http://thumb.1010pic.com/pic5/latex/104679.png)
如图2所示,
![](http://thumb.1010pic.com/pic5/latex/58451.png)
![](http://thumb.1010pic.com/pic5/latex/559.png)
∵
![](http://thumb.1010pic.com/pic5/latex/104679.png)
![](http://thumb.1010pic.com/pic5/latex/559.png)
∴蚂蚁所行的最短路线为
![](http://thumb.1010pic.com/pic5/latex/104679.png)
故答案为:
![](http://thumb.1010pic.com/pic5/latex/104679.png)
点评:本题是一道趣味题,将长方体展开,根据两点之间线段最短,运用勾股定理解答即可.
![](http://thumb2018.1010pic.com/images/loading.gif)
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