怎么求矩形对角线的长度

对角线是连接矩形的一个角及其对角的一条直线。^[1] 一个矩形有两条对角线，它们长度相等。^[2] 如果知道矩形各边的边长，你可以借助勾股定理轻易地算出对角线的长度，因为对角线将矩形分成了两个直角三角形。如果你不知道边长，但知道面积和周长，或边长之间的关系等其他信息，你可以先计算出矩形的长和宽，然后再用勾股定理算出对角线的长度。

步骤

使用长和宽

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/71\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-1-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-1-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/71\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-1-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 列出勾股定理的公式。该公式是${\displaystyle a^2+b^2=c^2}$，其中${\displaystyle a}$和${\displaystyle b}$是直角三角形直角边的边长，而${\displaystyle c}$是直角三角形的斜边长度。^[3]
   • 由于对角线将矩形切成了两个完全一样的直角三角形，所以你可以使用勾股定理。^[4] 矩形的长和宽是三角形的直角边；对角线是三角形的斜边。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/f\/fe\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-2-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-2-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/f\/fe\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-2-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-2-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 将长和宽代入到公式中。长和宽应该是已知条件，又或者你可以量出它们的长度。确保你用长和宽代入的是${\displaystyle a}$和${\displaystyle b}$。
   • 例如，如果矩形的宽是3 cm，而长是4 cm，代入公式后得到如下等式：${\displaystyle 3^2+4^2=c^2}$。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/b9\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-3-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-3-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/b9\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-3-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 算出长和宽的平方，然后相加求和。记住，一个数的平方等于用这个数乘以自己。
   • 例如：
     ${\displaystyle 3^2+4^2=c^2}$
     ${\displaystyle 9+16=c^2}$
     ${\displaystyle 25=c^2}$
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/1c\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-4-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-4-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/1c\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-4-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 将等式两边开平方。最简单的计算平方根的方法是使用计算器。如果你没有科学计算器，可以使用在线计算器。^[5] 这样可以算出${\displaystyle c}$的值，即三角形的斜边，也就是矩形对角线的长度。
   • 例如：
     ${\displaystyle 25=c^2}$
     ${\displaystyle \sqrt{25}=\sqrt{c^2}}$
     ${\displaystyle 5=c}$
     因此，宽为3 cm，而长为4 cm的矩形，其对角线的长度是5 cm。

使用面积和周长

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d9\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-5-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-5-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d9\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-5-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-5-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 列出矩形的面积公式。该公式是${\displaystyle A=lw}$，其中${\displaystyle A}$为矩形的面积，${\displaystyle l}$为矩形的长，而${\displaystyle w}$为矩形的宽。^[6]
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/b1\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-6-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-6-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/b1\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-6-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-6-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 将矩形的面积代入到公式中。确保你代入的是变量${\displaystyle A}$。
   • 例如，如果矩形的面积是35平方厘米，则代入后得到如下等式：${\displaystyle 35=lw}$。
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d3\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-7-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-7-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d3\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-7-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 变换等式，使之变成$$w{\displaystyle w}的表达式。等式两边都除以${\displaystyle l}$。将这个表达式放到一边。稍后你会将它代入周长公式。
   • 例如：
     ${\displaystyle 35=lw}$
     ${\displaystyle \frac{35}{l}=w}$。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/7\/7d\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-8-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-8-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/7\/7d\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-8-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 列出矩形的周长公式。该公式是${\displaystyle P=2(w+l)}$，其中${\displaystyle w}$为矩形的宽，而${\displaystyle l}$为矩形的长。^[7]
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/0\/02\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-9-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-9-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/0\/02\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-9-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-9-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 将周长的值代入到公式中。确保你代入的是变量${\displaystyle P}$。
   • 例如，如果矩形的周长是24厘米，则代入后会得到如下等式：${\displaystyle 24=2(w+l)}$。
6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/11\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-10-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-10-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/11\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-10-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-10-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 等式两边都除以2。这样就算出了${\displaystyle w+l}$的值。
   • 例如：
     ${\displaystyle 24=2(w+l)}$
     ${\displaystyle \frac{24}{2}=\frac{2(w+l)}{2}}$
     ${\displaystyle 12=w+l}$。
7. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/28\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-11-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-11-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/28\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-11-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-11-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 7 将$$w{\displaystyle w}的表达式代入到等式中。使用你变换面积公式得到的表达式。
   • 例如，如果使用你变换而得的表达式${\displaystyle \frac{35}{l}=w}$，把它代入周长公式中的${\displaystyle w}$：
     ${\displaystyle 12=w+l}$
     ${\displaystyle 12=\frac{35}{l}+l}$
8. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/1e\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-12-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-12-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/1e\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-12-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-12-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 8 去掉等式中的分母。等式两边都乘以${\displaystyle l}$。
   • 例如：
     ${\displaystyle 12=\frac{35}{l}+l}$
     ${\displaystyle 12\times l=(\frac{35}{l}\times l)+(l\times l)}$
     ${\displaystyle 12l=35+l^2}$
9. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/61\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-13-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-13-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/61\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-13-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-13-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 9 使等式一边等于0。等式两边都减去一次项。
   • 例如：
     ${\displaystyle 12l=35+l^2}$
     ${\displaystyle 12l-12l=35+l^2-12l}$
     ${\displaystyle 0=35+l^2-12l}$
10. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/4\/4b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-14-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-14-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/4\/4b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-14-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-14-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 10 按项次对等式重新排序。这意味着带指数的项排第一个，然后是带变量的项，最后是常量。重新排序时，请注意保留正确的正、负符号。你应该注意到了，这个等式现在变成了一个二次方程。
    • 例如，${\displaystyle 0=35+l^2-12l}$变成了${\displaystyle 0=l^2-12l+35}$。
11. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/1\/1f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-15-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-15-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/1\/1f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-15-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-15-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 11 将二次方程因式分解。关于如何进行此步骤的完整说明，请阅读解二次方程。
    • 例如，方程${\displaystyle 0=l^2-12l+35}$可因式分解成${\displaystyle 0=(l-7)(l-5)}$。
12. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/39\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-16-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-16-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/39\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-16-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-16-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 12 求$$l{\displaystyle l}的值。令各项等于零，求出变量。你会得到方程的两个解，或两个根。由于你面对的是一个矩形，所以得到的两个根是矩形的宽和长。
    • 例如：
      ${\displaystyle 0=(l-7)}$
      ${\displaystyle 7=l}$
      及
      ${\displaystyle 0=(l-5)}$
      ${\displaystyle 5=l}$。
      因此，矩形的长和宽分别为7 cm和5 cm。
13. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/35\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-17-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-17-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/35\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-17-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-17-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 13 列出勾股定理的公式。该公式是${\displaystyle a^2+b^2=c^2}$，其中${\displaystyle a}$和${\displaystyle b}$是直角三角形直角边的边长，而${\displaystyle c}$是直角三角形斜边的边长。^[8]
    • 由于对角线将矩形切成了两个完全一样的直角三角形，所以你可以使用勾股定理。^[9] 矩形的宽和长是三角形的直角边；对角线是三角形的斜边。
14. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/aa\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-18-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-18-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/aa\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-18-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-18-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 14 将宽和长代入到公式中。此时，长可以随意代入到a或b中，将宽代入另一个即可。
    • 例如，如果你算出矩形的宽和长为5 cm和7 cm，代入后得到如下等式：${\displaystyle 5^2+7^2=c^2}$。
15. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-19-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-19-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-19-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-19-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 15 算出宽和长的平方，然后相加求和。记住，一个数的平方等于用这个数乘以自己。
    • 例如：
      ${\displaystyle 5^2+7^2=c^2}$
      ${\displaystyle 25+49=c^2}$
      ${\displaystyle 74=c^2}$
16. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-20-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-20-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3f\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-20-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-20-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 16 将等式两边开平方。最简单的计算平方根的方法是使用计算器。如果你没有科学计算器，可以使用在线计算器。^[10] 这样可以算出${\displaystyle c}$的值，即三角形的斜边，也就是矩形对角线的长度。
    • 例如：
      ${\displaystyle 74=c^2}$
      ${\displaystyle \sqrt{74}=\sqrt{c^2}}$
      ${\displaystyle 8.6024=c}$
      因此，面积为${\displaystyle 35c{m}^2}$而周长为24 cm的矩形，其对角线长度约等于8.6 cm。

使用面积和边长的相对关系

1. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/e\/ea\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-21-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-21-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/e\/ea\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-21-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-21-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 1 写下能够说明两条边边长之间关系的等式。^[11] 你可以将之写成长(${\displaystyle l}$)或宽(${\displaystyle w}$)的表达式。将这个等式放到一边。稍后你会将它代入面积公式。
   • 例如，如果已知矩形的宽比矩形的长要长2 cm，你可以列出${\displaystyle w}$的表达式：${\displaystyle w=l+2}$。
2. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/af\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-22-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-22-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/af\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-22-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-22-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 2 列出矩形的面积公式。该公式是${\displaystyle A=lw}$，其中${\displaystyle A}$为矩形的面积，${\displaystyle l}$为矩形的长，而${\displaystyle w}$为矩形的宽。^[12]
   • 如果知道矩形的周长，你也可以使用这种方法，不过列出的应该是周长公式，而非面积公式。矩形的周长公式是${\displaystyle P=2(w+l)}$，其中${\displaystyle w}$为矩形的宽，而${\displaystyle l}$为矩形的长。^[13]
3. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/23\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-23-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-23-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/23\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-23-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-23-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 3 将矩形的面积代入到公式中。确保你代入的是变量${\displaystyle A}$。
   • 例如，如果矩形的面积是35平方厘米，则代入后得到如下等式：${\displaystyle 35=lw}$。
4. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/3b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-24-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-24-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/3b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-24-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-24-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 4 将长或宽的关系表达式代入公式中。由于你面对的是一个矩形，所以求${\displaystyle l}$或${\displaystyle w}$变量的值都可以。
   • 例如，如果你知道${\displaystyle w=l+2}$，可以将这个表达式代入面积公式中的${\displaystyle w}$：
     ${\displaystyle 35=lw}$
     ${\displaystyle 35=l(l+2)}$
5. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/96\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-25-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-25-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/96\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-25-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-25-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 5 列出二次方程。用括号前的系数乘以括号内的各项，然后使方程的一边等于0。
   • 例如：
     ${\displaystyle 35=l(l+2)}$
     ${\displaystyle 35=l^2+2l}$
     ${\displaystyle 0=l^2+2l-35}$
6. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/b\/bf\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-26-Version-3.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-26-Version-3.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/b\/bf\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-26-Version-3.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-26-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 6 将二次方程因式分解。关于如何进行此步骤的完整说明，请阅读解二次方程。
   • 例如，方程${\displaystyle 0=l^2+2l-35}$可因式分解成${\displaystyle 0=(l+7)(l-5)}$。
7. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/9b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-27-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-27-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/9b\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-27-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-27-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 7 求$$l{\displaystyle l}的值。令各项等于零，求出变量。你会求出方程的两个解，或两个根。
   • 例如：
     ${\displaystyle 0=(l+7)}$
     ${\displaystyle -7=l}$
     及
     ${\displaystyle 0=(l-5)}$
     ${\displaystyle 5=l}$。
     在本例中，你会得到一个负数根。由于矩形的长不可能为负数，所以长必定为5 cm。
8. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/2\/2d\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-28-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-28-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/2\/2d\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-28-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-28-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 8 将长或宽的值代入到关系表达式中。这样就算出了矩形另一条边的边长。
   • 例如，如果你知道矩形的长为5 cm， 且边长之间的关系为${\displaystyle w=l+2}$，可以将长的值5代入到表达式中：
     ${\displaystyle w=l+2}$
     ${\displaystyle w=5+2}$
     ${\displaystyle w=7}$
9. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/ac\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-29-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-29-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/ac\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-29-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-29-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 9 列出勾股定理的公式。该公式是${\displaystyle a^2+b^2=c^2}$，其中${\displaystyle a}$和${\displaystyle b}$是直角三角形直角边的边长，而${\displaystyle c}$是直角三角形斜边的边长。^[14]
   • 由于对角线将矩形切成了两个完全一样的直角三角形，所以你可以使用勾股定理。^[15] 矩形的宽和长是三角形的直角边；对角线是三角形的斜边。
10. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/3\/31\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-30-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-30-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/3\/31\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-30-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-30-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 10 将宽和长代入到公式中。此时，长可以随意代入到a或b中，将宽代入另一个即可。
    • 例如，如果你算出矩形的宽和长为5 cm和7 cm，代入后得到如下等式：${\displaystyle 5^2+7^2=c^2}$。
11. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/87\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-31-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-31-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/87\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-31-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-31-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 11 算出宽和长的平方，然后相加求和。记住，一个数的平方等于用这个数乘以自己。
    • 例如：
      ${\displaystyle 5^2+7^2=c^2}$
      ${\displaystyle 25+49=c^2}$
      ${\displaystyle 74=c^2}$
12. {"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/d\/d2\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-32-Version-2.jpg\/v4-460px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-32-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/d\/d2\/Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-32-Version-2.jpg\/v4-728px-Find-the-Measurement-of-the-Diagonal-Inside-a-Rectangle-Step-32-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"} 12 将等式两边开平方。最简单的计算平方根的方法是使用计算器。如果你没有科学计算器，可以使用在线计算器。^[16] 这样可以算出${\displaystyle c}$的值，即三角形的斜边，也就是矩形对角线的长度。
    • 例如：
      ${\displaystyle 74=c^2}$
      ${\displaystyle \sqrt{74}=\sqrt{c^2}}$
      ${\displaystyle 8.6024=c}$
      因此，宽比长要长2 cm，且面积为${\displaystyle 35c{m}^2}$的矩形，其对角线的长度约等于8.6 cm。