Given here is an equilateral triangle of side length a, which inscribes a hexagon which in turn inscribes a square. The task is to find the side length of the square.
Examples:
Input: a = 6 Output: 2.538 Input: a = 8 Output: 3.384
Approach:
We know the, side length of a hexagon inscribed within an equilateral triangle is h = a/3. Please refer Largest hexagon that can be inscribed within an equilateral triangle .
Also, the side length of the square that can be inscribed within a hexagon is x = 1.268h Please refer Largest Square that can be inscribed within a hexagon.
So, side length of the square inscribed within a hexagon which in turn is inscribed within an equilateral triangle, x = 0.423a.
Below is the implementation of the above approach:
C++
// C++ program to find the side of the largest square// that can be inscribed within the hexagon which in return// is incsribed within an equilateral triangle#include <bits/stdc++.h>using namespace std;// Function to find the side// of the squarefloat squareSide(float a){ // Side cannot be negative if (a < 0) return -1; // side of the square float x = 0.423 * a; return x;}// Driver codeint main(){ float a = 8; cout << squareSide(a) << endl; return 0;} |
Java
// Java program to find the side of the// largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangleclass cfg { // Function to find the side// of the squarestatic float squareSide(float a){ // Side cannot be negative if (a < 0) return -1; // side of the square float x = (0.423f * a); return x;}// Driver codepublic static void main(String[] args){ float a = 8; System.out.println(squareSide(a));}}// This code is contributed by // Mukul Singh. |
Python3
# Python 3 program to find the side of the # largest square that can be inscribed # within the hexagon which in return# is incsribed within an equilateral triangle# Function to find the side of the squaredef squareSide(a): # Side cannot be negative if (a < 0): return -1 # side of the square x = 0.423 * a return x# Driver codeif __name__ == '__main__': a = 8 print(squareSide(a))# This code is contributed by# Sanjit_Prasad |
C#
// C# program to find the side of the// largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangleusing System;class GFG{ // Function to find the side// of the squarestatic float squareSide(float a){ // Side cannot be negative if (a < 0) return -1; // side of the square float x = (0.423f * a); return x;}// Driver codepublic static void Main(){ float a = 8; Console.WriteLine(squareSide(a));}}// This code is contributed by // shs |
PHP
<?php// PHP program to find the side of the // largest square that can be inscribed // within the hexagon which in return is// incsribed within an equilateral triangle// Function to find the side of the squarefunction squareSide($a){ // Side cannot be negative if ($a < 0) return -1; // side of the square $x = 0.423 * $a; return $x;}// Driver code$a = 8;echo squareSide($a);// This code is contributed by ajit.?> |
Javascript
<script>// javascript program to find the side of the// largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangle// Function to find the side// of the squarefunction squareSide(a){ // Side cannot be negative if (a < 0) return -1; // side of the square var x = (0.423 * a); return x;}// Driver codevar a = 8;document.write(squareSide(a));// This code is contributed by Princi Singh </script> |
3.384
Time Complexity: O(1) since no loop is used the algorithm takes constant time to finish its execution
Auxiliary Space: O(1) since no extra array is used the space required by the algorithm to complete is constant.
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