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1 . 我国后汉时期的数学家赵爽通过弦图利用出入相补法证明了勾股定理,在我国历史上还有多人通过出入相补法证明过勾股定理,如下图为我国清末数学家华蘅芳证明勾股定理时构造的图形,在该图中
是以
为斜边的直角三角形,分别以
为边作3个正方形,点
在直线
上,
,记
的周长与面积分别为
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0e08a39c6619123557148d195abfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9c4e14fcf121dca94b9a5549a93288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de8fa2fa9271308932731a418f21f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f484be7264a86c5dcfe4e25d6459ac43.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/670c1694-0cdb-4130-9fd8-cc9450265163.png?resizew=168)
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