Given here is an equilateral triangle of side length a. The task is to find the side of the biggest square that can be inscribed within it.
Examples:
Input: a = 5 Output: 2.32 Input: a = 7 Output: 3.248
Approach: Let the side of the square be x.
Now, AH is perpendicular to DE.
DE is parallel to BC, So, angle AED = angle ACB = 60
In triangle EFC,
=> Sin60 = x/ EC
=> ?3 / 2 = x/EC
=> EC = 2x/?3
In triangle AHE,
=> Cos 60 = x/2AE
=> 1/2 = x/2AE
=> AE = x
So, side AC of the triangle = 2x/?3 + x. Now,
a = 2x/?3 + x
Therefore, x = a/(1 + 2/?3) = 0.464a
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest square// which can be inscribed within the equilateral triangle#include <bits/stdc++.h>using namespace std;// Function to find the side// of the squarefloat square(float a){ // the side cannot be negative if (a < 0) return -1; // side of the square float x = 0.464 * a; return x;}// Driver codeint main(){ float a = 5; cout << square(a) << endl; return 0;} |
Java
// Java Program to find the // the biggest square which// can be inscribed within // the equilateral triangleclass GFG{ // Function to find the side // of the square static double square(double a) { // the side cannot be negative if (a < 0) return -1; // side of the square double x = 0.464 * a; return x; } // Driver code public static void main(String []args) { double a = 5; System.out.println(square(a)); }}// This code is contributed by ihritik |
Python3
# Python3 Program to find the biggest square# which can be inscribed within the equilateral triangle# Function to find the side# of the squaredef square( a ): # the side cannot be negative if (a < 0): return -1 # side of the square x = 0.464 * a return x# Driver codea = 5print(square(a))# This code is contributed by ihritik |
C#
// C# Program to find the biggest // square which can be inscribed // within the equilateral triangleusing System;class GFG{ // Function to find the side // of the square static double square(double a) { // the side cannot be negative if (a < 0) return -1; // side of the square double x = 0.464 * a; return x; } // Driver code public static void Main() { double a = 5; Console.WriteLine(square(a)); }}// This code is contributed by ihritik |
PHP
<?php// PHP Program to find the biggest// square which can be inscribed // within the equilateral triangle// Function to find the side// of the squarefunction square($a ){ // the side cannot be negative if ($a < 0) return -1; // side of the square $x = 0.464 * $a; return $x;}// Driver code$a = 5;echo square($a);// This code is contributed by ihritik?> |
Javascript
<script>// javascript Program to find the // the biggest square which// can be inscribed within // the equilateral triangle// Function to find the side// of the squarefunction square(a){ // the side cannot be negative if (a < 0) return -1; // side of the square var x = 0.464 * a; return x;}// Driver code var a = 5; document.write(square(a).toFixed(2));// This code contributed by Princi Singh </script> |
Output:
2.32
Time Complexity: O(1)
Auxiliary Space: O(1)
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