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Program to find the shortest distance between diagonal and edge skew of a Cube

  • Difficulty Level : Medium
  • Last Updated : 17 Mar, 2021

Given an integer A, denoting the length of a cube, the task is to find the shortest distance between the diagonal of a cube and an edge skew to it i.e. KL in the below figure.

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Examples :



Input: A = 2
Output: 1.4142
Explanation:
Length of KL = A / √2
Length of KL = 2 / 1.41 = 1.4142

Input: A = 3
Output: 2.1213

Approach: The idea to solve the problem is based on the following mathematical formula:

Let’s draw a perpendicular from K to down face of cube as Q.
Using Pythagorean Theorem in triangle QKL,

KL2 = QK2 + QL2

l2 = (a/2)2 + (a/2)2 

l2 = 2 * (a/2)2

l = a / sqrt(2)

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the shortest distance
// between the diagonal of a cube and
// an edge skew to it
float diagonalLength(float a)
{
    // Stores the required distance
    float L = a / sqrt(2);
 
    // Print the required distance
    cout << L;
}
 
// Driver Code
int main()
{
    // Given side of the cube
    float a = 2;
 
    // Function call to find the shortest
    // distance between the diagonal of a
    // cube and an edge skew to it
    diagonalLength(a);
 
    return 0;
}

Java




// Java program for the above approach
 
class GFG {
 
    // Function to find the shortest
    // distance between the diagonal of a
    // cube and an edge skew to it
    static void diagonalLength(float a)
    {
        // Stores the required distance
        float L = a / (float)Math.sqrt(2);
 
        // Print the required distance
        System.out.println(L);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given side of the cube
        float a = 2;
 
        // Function call to find the shortest
        // distance between the diagonal of a
        // cube and an edge skew to it
        diagonalLength(a);
    }
}

Python3




# Python3 program for the above approach
 
from math import sqrt
 
# Function to find the shortest
# distance between the diagonal of a
# cube and an edge skew to it
def diagonalLength(a):
   
    # Stores the required distance
    L = a / sqrt(2)
 
    # Print the required distance
    print(L)
 
 
# Given side of the cube
a = 2
 
# Function call to find the shortest
# distance between the diagonal of a
# cube and an edge skew to it
diagonalLength(a)

C#




// C# program for the above approach
 
using System;
class GFG {
 
    // Function to find the shortest
    // distance between the diagonal of a
    // cube and an edge skew to it
    static void diagonalLength(float a)
    {
        // Stores the required distance
        float L = a / (float)Math.Sqrt(2);
 
        // Print the required distance
        Console.Write(L);
    }
 
    // Driver Code
    public static void Main()
    {
        // Given side of the cube
        float a = 2;
 
        // Function call to find the shortest
        // distance between the diagonal of a
        // cube and an edge skew to it
        diagonalLength(a);
    }
}

PHP




<?php
// PHP program for the above approach
   
// Function to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
function diagonalLength($a)
{
    // Stores the required distance
    $L = $a / sqrt(2);
 
    # Print the required distance
    echo $L;
}
 
// Given side of the cube
$a = 2;
 
// Function call to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
diagonalLength($a);
 
?>

Javascript




<script>
// javascript program for the above approach
 
// Function to find the shortest distance
// between the diagonal of a cube and
// an edge skew to it
function diagonalLength( a)
{
 
    // Stores the required distance
    let L = a / Math.sqrt(2);
 
    // Print the required distance
     document.write( L.toFixed(5));
}
 
// Driver Code
 
    // Given side of the cube
    let a = 2;
 
    // Function call to find the shortest
    // distance between the diagonal of a
    // cube and an edge skew to it
    diagonalLength(a);
 
// This code is contributed by todaysgaurav
 
</script>
Output: 
1.41421

 

Time Complexity: O(1)
Auxiliary Space: O(1)




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