任何长方体的所有 12 条边的长度之和

鉴于长方体，其具有一个共同的顶点的三个面的面积。我们的任务是找到这个平行六面体的所有 12 条边的长度之和。
在几何学中，平行六面体是由六个平行四边形构成的三维图形。以此类推，它涉及平行四边形，就像立方体涉及正方形或长方体涉及矩形一样。长方体的图片如下所示。

例子：

Input: 1 1 1 
Output: 12

Input: 20 10 50
Output: 68

方法：给定的区域是 s1, s2 和 s3 。设 a、b 和 c 是具有一个公共顶点的边的长度。在哪里$s1 = a * b$ , $s2 = b * c$ , $s3 = c * a$ .根据面部区域很容易找到长度： $a = \sqrt{s1s3/s2}$ , $b = \sqrt{s1s2/s3}$ , $c = \sqrt{s2s3/s1}$ .答案将是所有 4 条边的总和，有 4 条边的长度等于 a、b 和 c。
在第一个例子中，给定的面积 s1 = 1，s2 = 1 和 s3 = 1。所以使用上述方法，a、b、c 的值将是 1。所以所有 12 条边的长度之和将是 4 * 3 = 12。
下面是上述方法的实现：

C++

// C++ program to illustrate
// the above problem
#include 
using namespace std;
 
// function to find the sum of
// all the edges of parallelepiped
double findEdges(double s1, double s2, double s3)
{
    // to calculate the length of one edge
    double a = sqrt(s1 * s2 / s3);
    double b = sqrt(s3 * s1 / s2);
    double c = sqrt(s3 * s2 / s1);
 
    // sum of all the edges of one side
    double sum = a + b + c;
 
    // net sum will be equal to the
    // summation of edges of all the sides
    return 4 * sum;
}
 
// Driver code
int main()
{
    // initialize the area of three
    // faces which has a common vertex
    double s1, s2, s3;
    s1 = 65, s2 = 156, s3 = 60;
 
    cout << findEdges(s1, s2, s3);
 
    return 0;
}

Java

// Java program to illustrate
// the above problem
 
import java.io.*;
 
class GFG {
   
// function to find the sum of
// all the edges of parallelepiped
static double findEdges(double s1, double s2, double s3)
{
    // to calculate the length of one edge
    double a = Math.sqrt(s1 * s2 / s3);
    double b = Math.sqrt(s3 * s1 / s2);
    double c = Math.sqrt(s3 * s2 / s1);
 
    // sum of all the edges of one side
    double sum = a + b + c;
 
    // net sum will be equal to the
    // summation of edges of all the sides
    return 4 * sum;
}
 
       // Driver code
 
    public static void main (String[] args) {
            // initialize the area of three
    // faces which has a common vertex
    double s1, s2, s3;
    s1 = 65; s2 = 156; s3 = 60;
 
    System.out.print(findEdges(s1, s2, s3));
    }
}
 
 
// this code is contributed by anuj_67..

Python3

import math
 
# Python3 program to illustrate
# the above problem
 
# function to find the sum of
# all the edges of parallelepiped
def findEdges(s1, s2, s3):
 
    # to calculate the length of one edge
    a = math.sqrt(s1 * s2 / s3)
    b = math.sqrt(s3 * s1 / s2)
    c = math.sqrt(s3 * s2 / s1)
 
    # sum of all the edges of one side
    sum = a + b + c
 
    # net sum will be equal to the
    # summation of edges of all the sides
    return 4 * sum
 
 
# Driver code
if __name__=='__main__':
     
# initialize the area of three
# faces which has a common vertex
    s1 = 65
    s2 = 156
    s3 = 60
 
    print(int(findEdges(s1, s2, s3)))
         
# This code is contributed by
# Shivi_Aggarwal

C#

// C# program to illustrate
// the above problem
using System;
 
public class GFG{
     
// function to find the sum of
// all the edges of parallelepiped
static double findEdges(double s1, double s2, double s3)
{
    // to calculate the length of one edge
    double a = Math.Sqrt(s1 * s2 / s3);
    double b = Math.Sqrt(s3 * s1 / s2);
    double c = Math.Sqrt(s3 * s2 / s1);
 
    // sum of all the edges of one side
    double sum = a + b + c;
 
    // net sum will be equal to the
    // summation of edges of all the sides
    return 4 * sum;
}
 
// Driver code
 
    static public void Main (){
    // initialize the area of three
    // faces which has a common vertex
    double s1, s2, s3;
    s1 = 65; s2 = 156; s3 = 60;
 
    Console.WriteLine(findEdges(s1, s2, s3));
    }
}
 
 
// This code is contributed by anuj_67..

Javascript

    // Javascript program to illustrate the above problem
     
    // function to find the sum of
    // all the edges of parallelepiped
    function findEdges(s1, s2, s3)
    {
        // to calculate the length of one edge
        let a = Math.sqrt(s1 * s2 / s3);
        let b = Math.sqrt(s3 * s1 / s2);
        let c = Math.sqrt(s3 * s2 / s1);
 
        // sum of all the edges of one side
        let sum = a + b + c;
 
        // net sum will be equal to the
        // summation of edges of all the sides
        return 4 * sum;
    }
     
    // initialize the area of three
    // faces which has a common vertex
    let s1, s2, s3;
    s1 = 65; s2 = 156; s3 = 60;
   
    document.write(findEdges(s1, s2, s3));
 

输出：

120

参考： https : //en.wikipedia.org/wiki/Parallelepiped