# 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. Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

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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 ``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

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## Javascript

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Output:
`1.41421`

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

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