题目内容
如图所示,在△ABC中,AC=5,中线AD=4,则AB边的取值范围是( ).
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231354337554464.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231354337554464.png)
B
本题考查三角形的三边关系
过点D作
交
于点
,由
为中线且
得,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433864710.png)
在
中,
,则由“三角形两边之和大于第三边”得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433989794.png)
又三角形两边之差小于第三边”得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434005769.png)
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434098685.png)
又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434114531.png)
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434130755.png)
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434161527.png)
故正确答案为B
过点D作
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433771558.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433818375.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433833312.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433833392.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433849363.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433864710.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433927534.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433942730.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135433989794.png)
又三角形两边之差小于第三边”得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434005769.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434098685.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434114531.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434130755.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135434161527.png)
故正确答案为B
![](http://thumb.zyjl.cn/images/loading.gif)
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A.![]() | B.![]() |
C.![]() | D.![]() |