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 = 10
Output: 14.1421
Explanation: The length of the diagonal of a square whose sides are of length 10 is 14.1421Input: S = 24
Output: 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)2 = (base)2 + (perpendicular)2, where D and S are length of the diagonal and the square.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 sidedouble findDiagonal(double s){ return sqrt(2) * s;}// Driver Codeint main(){ double S = 10; cout << findDiagonal(S); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to find the length of the// diagonal of a square of a given sidestatic double findDiagonal(double s){ return (double)Math.sqrt(2) * s;}// Driver Codepublic 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 approachimport math# Function to find the length of the# diagonal of a square of a given sidedef findDiagonal(s): return math.sqrt(2) * s# Driver Codeif __name__ == "__main__": S = 10 print(findDiagonal(S))# This code is contributed by chitranayal |
C#
// C# program for the above approachusing System;public class GFG{// Function to find the length of the// diagonal of a square of a given sidestatic double findDiagonal(double s){ return (double)Math.Sqrt(2) * s;}// Driver Codepublic 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 sidefunction findDiagonal(s){ return Math.sqrt(2) * s;}// Driver Codevar S = 10;document.write(findDiagonal(S).toFixed(6));// This code contributed by shikhasingrajput </script> |
14.1421
Time Complexity: O(1)
Auxiliary Space: O(1)
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