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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 14.1421
Input: 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++
#include <bits/stdc++.h>
using namespace std;
double findDiagonal(double s)
{
return sqrt(2) * s;
}
int main()
{
double S = 10;
cout << findDiagonal(S);
return 0;
}
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Java
import java.util.*;
class GFG{
static double findDiagonal(double s)
{
return (double)Math.sqrt(2) * s;
}
public static void main(String[] args)
{
double S = 10;
System.out.print(findDiagonal(S));
}
}
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Python3
import math
def findDiagonal(s):
return math.sqrt(2) * s
if __name__ == "__main__":
S = 10
print(findDiagonal(S))
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C#
using System;
public class GFG
{
static double findDiagonal(double s)
{
return (double)Math.Sqrt(2) * s;
}
public static void Main(String[] args)
{
double S = 10;
Console.Write(findDiagonal(S));
}
}
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Javascript
<script>
function findDiagonal(s)
{
return Math.sqrt(2) * s;
}
var S = 10;
document.write(findDiagonal(S).toFixed(6));
</script>
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Time Complexity: O(1)
Auxiliary Space: O(1)
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