Given an equilateral triangle of side length a, the task is to find the largest hexagon that can be inscribed within it.
Examples:
Input: a = 6
Output: 2
Input: a = 9
Output: 3
Approach: From the figure, it is clear that the three small triangles are also equilateral. So they will have side length b = a / 3 where b is also the length of the hexagon and a is the length of the given equilateral triangle.
Below is the implementation of the above approach:
C++
// C++ program to find the side of the // largest hexagon which can be inscribed // within an equilateral triangle #include <bits/stdc++.h> using namespace std;
// Function to find the side // of the hexagon float hexagonside( float a)
{ // Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
float x = a / 3;
return x;
} // Driver code int main()
{ float a = 6;
cout << hexagonside(a) << endl;
return 0;
} |
Java
// Java program to find the side of the // largest hexagon which can be inscribed // within an equilateral triangle class CLG
{ // Function to find the side // of the hexagon static float hexagonside( float a)
{ // Side cannot be negative
if (a < 0 )
return - 1 ;
// Side of the hexagon
float x = a / 3 ;
return x;
} // Driver code public static void main(String[] args)
{ float a = 6 ;
System.out.println(hexagonside(a));
} } |
Python3
# Python3 program to find the side of the # largest hexagon which can be inscribed # within an eqilateral triangle # function to find the side of the hexagon def hexagonside(a):
# Side cannot be negative
if a < 0 :
return - 1
# Side of the hexagon
x = a / / 3
return x
# Driver code a = 6
print (hexagonside(a))
# This code is contributed # by Mohit kumar 29 |
C#
using System;
// C# program to find the side of the // largest hexagon which can be inscribed // within an equilateral triangle class CLG
{ // Function to find the side // of the hexagon static float hexagonside( float a)
{ // Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
float x = a / 3;
return x;
} // Driver code public static void Main()
{ float a = 6;
Console.Write(hexagonside(a));
} } |
PHP
<?php // PHP program to find the side of the // largest hexagon which can be inscribed // within an equilateral triangle // Function to find the side // of the hexagon function hexagonside( $a )
{ // Side cannot be negative
if ( $a < 0)
return -1;
// Side of the hexagon
$x = $a / 3;
return $x ;
} // Driver code $a = 6;
echo hexagonside( $a ) ;
// This code is contributed by Ryuga ?> |
Javascript
<script> // javascript program to find the side of the // largest hexagon which can be inscribed // within an equilateral triangle // Function to find the side // of the hexagon function hexagonside(a)
{ // Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
var x = a / 3;
return x;
} // Driver code var a = 6;
document.write(hexagonside(a)); // This code contributed by Princi Singh </script> |
Output:
2
Time Complexity: O(1)
Auxiliary Space: O(1)