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 1
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
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++ 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 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 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.. |
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# 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.. |
<?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 calculate 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 ?> |
// 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;
} // Driver code // initialize the area of three // faces which has a common vertex let s1 = 65, s2 = 156, s3 = 60; console.log(findEdges(s1, s2, s3)); //This code is contributed by chinmaya121221 |
Output:
120
Time Complexity: O(logn) because the inbuilt sqrt function is being used
Auxiliary Space: O(1)