任何长方体的所有12条边的长度总和

鉴于长方体，其具有一个共同的顶点的三个面的面积。我们的任务是找到此平行六面体的所有12个边的长度之和。

在几何形状中，平行六面体是由六个平行四边形形成的三维图形。类似地，它与平行四边形有关，就像立方体与正方形有关或作为长方体涉及矩形一样。矩形平行六面体的图片如下所示。

例子：

Input: 1 1 1 
Output: 12

Input: 20 10 50
Output: 68

方法：给定的面积为s1，s2和s3。设a，b和c为具有一个共同顶点的边的长度。在哪里$s1 = a * b$ ， $s2 = b * c$ ， $s3 = c * a$ 。很容易找到脸部区域的长度： $a = \sqrt{s1s3/s2}$ ， $b = \sqrt{s1s2/s3}$ ， $c = \sqrt{s2s3/s1}$ 。答案将是所有4个边的总和，有4个边的长度等于a，b和c。

在第一个示例中，给定的面积s1 = 1，s2 = 1且s3 =1。因此，采用上述方法，a，b，c的值将变为1。因此，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..

输出：

120

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