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: 2Input: 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 = 6print(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 ?> |
2
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