# Program to calculate length of diagonal of a square

Given a positive integer **S**, the task is to find the length of diagonal of a square having sides of length **S**.

**Examples:**

Input:S = 10Output:14.1421Explanation:The length of the diagonal of a square whose sides are of length 10 is 14.1421

Input:S = 24Output:33.9411

**Approach:** The given problem can be solved based on the mathematical relation between the length of sides of a square and the length of diagonal of a square as illustrated below:

As visible from the above image, the diagonal and the two sides of the square form a right-angled triangle. Therefore, by applying Pythagoras Theorem:

(hypotenuse), where D and S are length of the diagonal and the square.^{2}= (base)^{2}+ (perpendicular)^{2}Therefore,

=>

=>

=>

Therefore, simply calculate the length of the diagonal using the above-derived relation.

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 length of the` `// diagonal of a square of a given side` `double` `findDiagonal(` `double` `s)` `{` ` ` `return` `sqrt` `(2) * s;` `}` `// Driver Code` `int` `main()` `{` ` ` `double` `S = 10;` ` ` `cout << findDiagonal(S);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to find the length of the` `// diagonal of a square of a given side` `static` `double` `findDiagonal(` `double` `s)` `{` ` ` `return` `(` `double` `)Math.sqrt(` `2` `) * s;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `double` `S = ` `10` `;` ` ` ` ` `System.out.print(findDiagonal(S));` `}` `}` `// This code is contributed by splevel62` |

## Python3

`# Python3 program for the above approach` `import` `math` `# Function to find the length of the` `# diagonal of a square of a given side` `def` `findDiagonal(s):` ` ` ` ` `return` `math.sqrt(` `2` `) ` `*` `s` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `S ` `=` `10` ` ` ` ` `print` `(findDiagonal(S))` `# This code is contributed by chitranayal` |

## C#

`// C# program for the above approach` `using` `System;` `public` `class` `GFG` `{` `// Function to find the length of the` `// diagonal of a square of a given side` `static` `double` `findDiagonal(` `double` `s)` `{` ` ` `return` `(` `double` `)Math.Sqrt(2) * s;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `double` `S = 10;` ` ` ` ` `Console.Write(findDiagonal(S));` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// JavaScript program for the above approach` `// Function to find the length of the` `// diagonal of a square of a given side` `function` `findDiagonal(s)` `{` ` ` `return` `Math.sqrt(2) * s;` `}` `// Driver Code` `var` `S = 10;` `document.write(findDiagonal(S).toFixed(6));` `// This code contributed by shikhasingrajput` `</script>` |

**Output:**

14.1421

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