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.Â
Examples:Â
Input: 1 1 1Â
Output: 12Input: 20 10 50
Output: 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:Â Â
C++
// C++ program to illustrate// the above problem#include <bits/stdc++.h>using namespace std;Â
// function to find the sum of// all the edges of parallelepipeddouble 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);Â
    // sum of all the edges of one side    double sum = a + b + c;Â
    // net sum will be equal to the    // summation of edges of all the sides    return 4 * sum;}Â
// Driver codeint main(){    // initialize the area of three    // faces which has a common vertex    double s1, s2, s3;    s1 = 65, s2 = 156, s3 = 60;Â
    cout << findEdges(s1, s2, s3);Â
    return 0;} |
Java
// Java program to illustrate// the above problemÂ
import java.io.*;Â
class GFG {   // function to find the sum of// all the edges of parallelepipedstatic 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);Â
    // sum of all the edges of one side    double sum = a + b + c;Â
    // net sum will be equal to the    // summation of edges of all the sides    return 4 * sum;}Â
       // Driver codeÂ
    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;Â
    System.out.print(findEdges(s1, s2, s3));    }}Â
Â
// this code is contributed by anuj_67.. |
Python3
import mathÂ
# Python3 program to illustrate# the above problemÂ
# function to find the sum of# all the edges of parallelepipeddef findEdges(s1, s2, s3):Â
    # 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)Â
    # sum of all the edges of one side    sum = a + b + cÂ
    # net sum will be equal to the    # summation of edges of all the sides    return 4 * sumÂ
Â
# Driver codeif __name__=='__main__':     # initialize the area of three# faces which has a common vertex    s1 = 65    s2 = 156    s3 = 60Â
    print(int(findEdges(s1, s2, s3)))         # This code is contributed by # Shivi_Aggarwal |
C#
// C# program to illustrate// the above problemusing System;Â
public class GFG{     // function to find the sum of// all the edges of parallelepipedstatic 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);Â
    // sum of all the edges of one side    double sum = a + b + c;Â
    // net sum will be equal to the    // summation of edges of all the sides    return 4 * sum;}Â
// Driver codeÂ
    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;Â
    Console.WriteLine(findEdges(s1, s2, s3));    }}Â
Â
// This code is contributed by anuj_67.. |
PHP
<?php// PHP program to illustrate// the above problemÂ
// function to find the sum of// all the edges of parallelepipedfunction findEdges($s1, $s2, $s3){    // to calculate the length of one edge    $a = sqrt($s1 * $s2 / $s3);    $b = sqrt($s3 * $s1 / $s2);    $c = sqrt($s3 * $s2 / $s1);Â
    // sum of all the edges of one side    $sum = $a + $b + $c;Â
    // net sum will be equal to the    // summation of edges of all the sides    return 4 * $sum;}Â
// Driver codeÂ
// initialize the area of three// faces which has a common vertex$s1; $s2; $s3;$s1 = 65; $s2 = 156; $s3 = 60;Â
echo findEdges($s1, $s2, $s3);Â
// This code is contributed by Shashank?> |
Javascript
// JavaScript program to illustrate// the above problemÂ
// function to find the sum of// all the edges of parallelepipedfunction 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);Â
    // sum of all the edges of one side    let sum = a + b + c;Â
    // net sum will be equal to the    // summation of edges of all the sides    return 4 * sum;}Â
// Driver code// initialize the area of three// faces which has a common vertexlet s1 = 65, s2 = 156, s3 = 60;console.log(findEdges(s1, s2, s3));//This code is contributed by chinmaya121221 |
Output:Â
120
Â
Time Complexity: O(logn) because the inbuilt sqrt function is being used
Auxiliary Space: O(1)
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