《九章算术》勾股章[一五]问“勾股容方”描述了关于图形之间关系的问题:如图1,知道一个直角三角形较短直角边("勾")与较长直角边("股")的长度,那么,以该三角形的直角顶点为一个顶点、另外三个顶点分别在该三角形三边上的正方形的边长就可以求得.(我们不妨称这个正方形为该直角三角形的“所容正方形”)
其文如下:
题:今有勾五步,股十二步,问勾中容方几何?
答:方三步,十七分步之九.
术:并勾、股为法,勾、股相乘为实,实如法而一,得方一步.
“题”、“答”、“术”的意思大致如下:
问题:一个直角三角形两直角边的长分别为5和12,它的“所容正方形”的边长是多少?
答案:
.
解法:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269cd7ef3d0bc8f91886433a819dae09.png)
(1)已知:如图1,在
中,
,若
,则“所容正方形”
的边长为________.
请说明理由:
(2)应用(1)中的结论解决问题:
如图2,中山公园有一块菱形场地,其面积为19200m2,两条对角线长度之和为400m.现要在这个菱形场地上修建一个正方形花圃,并且要使正方形花圃的四个顶点分别落在菱形场地的四条边上,则该正方形花圃的边长为________m.
其文如下:
题:今有勾五步,股十二步,问勾中容方几何?
答:方三步,十七分步之九.
术:并勾、股为法,勾、股相乘为实,实如法而一,得方一步.
“题”、“答”、“术”的意思大致如下:
问题:一个直角三角形两直角边的长分别为5和12,它的“所容正方形”的边长是多少?
答案:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6aeb767ea82b782addd1a74ce518a.png)
解法:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269cd7ef3d0bc8f91886433a819dae09.png)
(1)已知:如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b40c2b0ab8e1cfe5112d428b4b829f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd6f9149d98ef0f0d7c1aab97d613f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec07464a1b5bc7a2cc338b1a13e0f4a6.png)
请说明理由:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/28/18681d66-fd6c-486c-920f-340d4048e4a6.png?resizew=312)
(2)应用(1)中的结论解决问题:
如图2,中山公园有一块菱形场地,其面积为19200m2,两条对角线长度之和为400m.现要在这个菱形场地上修建一个正方形花圃,并且要使正方形花圃的四个顶点分别落在菱形场地的四条边上,则该正方形花圃的边长为________m.
2023·山东青岛·二模 查看更多[2]
更新时间:2023-05-23 22:55:07
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【推荐2】如图,一次函数y=kx+b图像分别与x轴、y轴交于点A(8,0)、B(0,6),四边形ABCD是正方形.
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