# Find the diagonal of the Cube

Given a side of the cube **a**. The task is to find the length of the diagonal of the cube.

**Examples:**

Input :a = 3Output :5.19615Input :a = 6Output :10.3923

**Formula : **

Length of diagonal of the cube = sqrt(3) * side

**Proof :**

Use Pythagorean Theorem,

In triangle CED,

CE^{2}= CD^{2}+ DE^{2}

l^{2}= a^{2}+ a^{2}———>(1)

In triangle CFE,

CF^{2}= CE^{2}+ EF^{2}

L^{2}= l^{2}+ a^{2}

use l^{2}value from equation(1),

L^{2}= a^{2}+ a^{2}+ a^{2}

= 3*a^{2}

L = sqrt(3) * a

## C++

`// CPP program to find length` `// of the diagonal of the cube` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find length` `// of diagonal of cube` `float` `diagonal_length(` `float` `a)` `{` ` ` `float` `L;` ` ` `// Formula to Find length` ` ` `// of diagonal of cube` ` ` `L = a * ` `sqrt` `(3);` ` ` `return` `L;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 5;` ` ` `// Function call` ` ` `cout << diagonal_length(a);` ` ` `return` `0;` `}` |

## Java

`// Java program to find length` `// of the diagonal of the cube` `class` `GFG` `{` ` ` ` ` `// Function to find length` ` ` `// of diagonal of cube` ` ` `static` `float` `diagonal_length(` `float` `a)` ` ` `{` ` ` `float` `L;` ` ` ` ` `// Formula to Find length` ` ` `// of diagonal of cube` ` ` `L = a * (` `float` `)Math.sqrt(` `3` `);` ` ` ` ` `return` `L;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `float` `a = ` `5` `;` ` ` ` ` `// Function call` ` ` `System.out.println(diagonal_length(a));` ` ` `}` `}` `// This code is contributed by` `// sanjeev2552` |

## Python3

`# Python3 program to find length` `# of the diagonal of the cube` `from` `math ` `import` `sqrt` `# Function to find length` `# of diagonal of cube` `def` `diagonal_length(a):` ` ` `L ` `=` `0` ` ` `# Formula to Find length` ` ` `# of diagonal of cube` ` ` `L ` `=` `a ` `*` `sqrt(` `3` `)` ` ` `return` `L` `# Driver code` `a ` `=` `5` `# Function call` `print` `(diagonal_length(a))` `# This code is contributed by Mohit Kumar` |

## C#

`// C# program to find length` `// of the diagonal of the cube` `using` `System;` `class` `GFG` `{` `// Function to find length` `// of diagonal of cube` `static` `float` `diagonal_length(` `float` `a)` `{` ` ` `float` `L;` ` ` `// Formula to Find length` ` ` `// of diagonal of cube` ` ` `L = a * (` `float` `)Math.Sqrt(3);` ` ` `return` `L;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `float` `a = 5;` ` ` `// Function call` ` ` `Console.Write(diagonal_length(a));` `}` `}` `// This code is contributed by Nidhi` |

## PHP

`<?php` `// PHP program to find length` `// of the diagonal of the cube` `// Function to find length` `// of diagonal of cube` `function` `diagonal_length(` `$a` `)` `{` ` ` `$L` `;` ` ` `// Formula to Find length` ` ` `// of diagonal of cube` ` ` `$L` `= ` `$a` `* sqrt(3);` ` ` `return` `$L` `;` `}` `// Driver code` `$a` `= 5;` `// Function call` `echo` `diagonal_length(` `$a` `);` `// This code is contributed` `// by Naman_Garg.` `?>` |

## Javascript

`<script>` `// javascript program to find length` `// of the diagonal of the cube` `// Function to find length` `// of diagonal of cube` `function` `diagonal_length( a)` `{` ` ` `let L;` ` ` `// Formula to Find length` ` ` `// of diagonal of cube` ` ` `L = a * Math.sqrt(3);` ` ` `return` `L;` `}` `// Driver code` ` ` `let a = 5;` ` ` `// Function call` ` ` `document.write(diagonal_length(a).toFixed(5));` ` ` `// This code is contributed by gauravrajput1` `</script>` |

**Output:**

8.66025