题目内容
在
中,已知
,面积
,
(1)求
的三边的长;
(2)设
是
(含边界)内的一点,
到三边
的距离分别是![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032741469.png)
①写出
所满足的等量关系;
②利用线性规划相关知识求出
的取值范围.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032101544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032304625.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032507740.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032538617.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032101544.png)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032585289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032101544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032585289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032725615.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032741469.png)
①写出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032741469.png)
②利用线性规划相关知识求出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032788471.png)
(1)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033115539.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032913669.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033115539.png)
第一问中利用设
中角
所对边分别为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033381451.png)
由
得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033412848.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033459569.png)
又由
得
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033552417.png)
又由
得
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033552417.png)
又
又
得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034005336.png)
即
的三边长![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032913669.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343012177.png)
第二问中,①
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343631039.png)
故![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034379761.png)
②![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343951619.png)
令
依题意有![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150344411090.png)
作图,然后结合区域得到最值。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150344574198.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032101544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033349473.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033381451.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032507740.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033412848.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033443674.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033459569.png)
又由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033474619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033490619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033537431.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033552417.png)
又由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033474619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033490619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033537431.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033552417.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033771912.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033802392.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215033817552.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034005336.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032101544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215032913669.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343012177.png)
第二问中,①
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034317864.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343631039.png)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034379761.png)
②
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150343951619.png)
令
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215034426539.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150344411090.png)
作图,然后结合区域得到最值。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232150344574198.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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