如图所示图案是我国汉代数学家赵爽在注解《周髀算经》时给出的,人们称它为”赵爽弦图“.已知AE=4,BE=3,若向正方形ABCD内随意投掷飞镖(每次均落在正方形ABCD内,且落在正方形ABCD内任何一点的机会均等),则恰好落在正方形EFGH内的概率为( )
![](https://img.xkw.com/dksih/QBM/2019/10/11/2309759964094464/2311895705509888/STEM/cb9618d0a3444002b2e4153f3138089b.png?resizew=109)
![](https://img.xkw.com/dksih/QBM/2019/10/11/2309759964094464/2311895705509888/STEM/cb9618d0a3444002b2e4153f3138089b.png?resizew=109)
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更新时间:2019-10-14 10:26:45
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【推荐1】我国汉代数学家赵爽为了证明勾股定理,创制了一幅“弦图”,后人称其为“赵爽弦图”,如图由“赵爽弦图”变化得到,它是用八个全等的直角三角形拼接而成,记图中正方形
,正方形
,正方形
的面积分别为
,
,
.若
,则
的值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/86f7531f-0d49-4ef7-9412-066817f09676.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28a58cd0be0267a309596d9866e65e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
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【推荐2】如图所示,是用4个全等的直角三角形与1个正方形镶嵌而成的正方形图案,已知大正方形面积为49,小正方形面积为4,若用
,
表示直角三角形的两直角边(
),下列四个说法:①
,②
,③
,④
.其中说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/8/31/2798236842450944/2803472210157568/STEM/bfc01d10-0005-4a8d-ad1a-31ca39b3db8e.png?resizew=117)
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【推荐1】“赵爽弦图”是由四个全等的直角三角形与中间的一个小正方形拼成的一个大正方形(如图所示).小亮同学随机地在大正方形及其内部区域投针,若直角三角形的两条直角边的长分别是2和1,则针扎到小正方形(阴影)区域的概率是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/e0e85cb0-a3d5-43ad-a505-5d0c7515063c.png?resizew=132)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/e0e85cb0-a3d5-43ad-a505-5d0c7515063c.png?resizew=132)
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【推荐2】如图,点D在
的边
上,连接
,点P的位置如图所示,在图中随机选择一个三角形,则点P在选择的三角形内部的概率是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/63620ed0-b327-40eb-9215-8ecbf21ff9d5.png?resizew=178)
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