Related Articles

# Biggest Square that can be inscribed within an Equilateral triangle

• Last Updated : 10 Mar, 2021

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 ``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;``}`

## Java

 `// 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`

## Python3

 `# 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`

## C#

 `// 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`

## PHP

 ``

## Javascript

 ``
Output:
`2.32`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up