题目内容
如图,某生态园欲把一块四边形地
辟为水果园,其中
,
,
.若经过
上一点
和
上一点
铺设一条道路
,且
将四边形
分成面积相等的两部分,设
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238143901623.png)
(1)求
的关系式;
(2)如果
是灌溉水管的位置,为了省钱,希望它最短,求
的长的最小值;
(3)如果
是参观路线,希望它最长,那么
的位置在哪里?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814171538.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814187656.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814202655.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814218573.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814234374.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814249289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814265416.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814280333.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814171538.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814374711.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238143901623.png)
(1)求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814405405.png)
(2)如果
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
(3)如果
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814499412.png)
(1)
;(2)
;(3)P点在B处,Q点在E处.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814514915.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814530550.png)
试题分析:(1)由题目条件可求出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814546535.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814577787.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814592538.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814405405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814639553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814405405.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814702266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814312399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814702266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238147481770.png)
试题解析:(1)易知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814546535.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814780689.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814795980.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238148262041.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238148421073.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238148581934.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814889928.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814904568.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238149201019.png)
(3)令
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238149361350.png)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238149511036.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814967807.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023814998836.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023815014462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023815029462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023815045552.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023815060606.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240238150761530.png)
此时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824023815076981.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目