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 = 5Output:2.32Input:a = 7Output: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 triangleEFC, => Sin60 = x/ EC => √3 / 2 = x/EC => EC = 2x/√3 In triangleAHE, => 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++ 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 square ` `float` `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 code ` `int` `main() `
`{ ` ` ` `float` `a = 5; `
` ` `cout << square(a) << endl; `
` ` ` ` `return` `0; `
`} ` |

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`// Java Program to find the ` `// the biggest square which ` `// can be inscribed within ` `// the equilateral triangle ` ` ` `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(String []args) `
` ` `{ `
` ` `double` `a = ` `5` `; `
` ` `System.out.println(square(a)); `
` ` `} `
`} ` ` ` `// This code is contributed by ihritik ` |

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`# Python3 Program to find the biggest square ` `# which can be inscribed within the equilateral triangle ` ` ` `# Function to find the side ` `# of the square ` `def` `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`
`print` `(square(a)) `
` ` `# This code is contributed by ihritik ` |

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`// C# Program to find the biggest ` `// square which can be inscribed ` `// within the equilateral triangle ` `using` `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 ` |

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`<?php ` `// PHP Program to find the biggest ` `// square which can be inscribed ` `// within the equilateral triangle ` ` ` `// Function to find the side ` `// of the square ` `function` `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 ` ` ` `?> ` |

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**Output:**

2.32

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