# Sum of lengths of all 12 edges of any rectangular parallelepiped

Given the area of three faces of the rectangular **parallelepiped** which has a common vertex. Our task is to find the **sum of lengths of all 12 edges** of this parallelepiped.

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms. By analogy, it relates to a parallelogram just as a cube relates to a square or as a cuboid to a rectangle. A picture of a rectangular parallelepiped is shown below.

**Examples:**

Input:1 1 1Output:12Input:20 10 50Output:68

**Approach: ** The area given are s1, s2 and s3 . Let a, b and c be the lengths of the sides that have one common vertex. Where , , . It’s easy to find the length in terms of faces areas: , , . The answer will be the summation of all the 4 sides, there are four sides that have lengths equal to a, b and c.

In the first example the given area s1 = 1, s2 = 1 and s3 = 1. So with the above approach, the value of a, b, c will come out to be 1. So the sum of the length of all 12 edges will be 4 * 3 = 12.

Below is the implementation of the above approach:

## C++

`// C++ program to illustrate ` `// the above problem ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function to find the sum of ` `// all the edges of parallelepiped ` `double` `findEdges(` `double` `s1, ` `double` `s2, ` `double` `s3) ` `{ ` ` ` `// to caculate 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; ` `} ` |

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## 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 caculate 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.. ` |

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## 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 caculate 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 ` |

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## 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 caculate 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.. ` |

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## PHP

`<?php ` `// PHP program to illustrate ` `// the above problem ` ` ` `// function to find the sum of ` `// all the edges of parallelepiped ` `function` `findEdges(` `$s1` `, ` `$s2` `, ` `$s3` `) ` `{ ` ` ` `// to caculate the length of one edge ` ` ` `$a` `= sqrt(` `$s1` `* ` `$s2` `/ ` `$s3` `); ` ` ` `$b` `= sqrt(` `$s3` `* ` `$s1` `/ ` `$s2` `); ` ` ` `$c` `= 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 ` ` ` `// initialize the area of three ` `// faces which has a common vertex ` `$s1` `; ` `$s2` `; ` `$s3` `; ` `$s1` `= 65; ` `$s2` `= 156; ` `$s3` `= 60; ` ` ` `echo` `findEdges(` `$s1` `, ` `$s2` `, ` `$s3` `); ` ` ` `// This code is contributed by Shashank ` `?> ` |

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**Output:**

120

**Reference:** https://en.wikipedia.org/wiki/Parallelepiped

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