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

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. 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 ` `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

 ` `

## Javascript

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Output:

`1.41421`

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

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