1 . 如图,有一个小矩形公园
,其中
,现过点
修建一条笔直的围墙(不计宽度)与
和
的延长线分别交于点
,现将小矩形公园扩建为三角形公园
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/21/655f0a57-117e-4c3d-be0d-9af80b773f80.png?resizew=200)
(1)当
多长时,才能使扩建后的公园
的面积最小?并求出
的最小面积.
(2)当扩建后的公园
的面积最小时,要对其进行规划,要求中间为三角形绿地(图中阴影部分),周围是等宽的公园健步道,如图所示. 若要保证绿地面积不小于总面积的
,求健步道宽度的最大值.(小数点后保留三位小数)
参考数据:
.
参考公式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9b5d77088c7b387af6e6b84ca53494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/21/655f0a57-117e-4c3d-be0d-9af80b773f80.png?resizew=200)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
(2)当扩建后的公园
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd06d31449f0692b8c1a9e347ac5816.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d00031d57f1592c6f000f91f82a84a.png)
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