# Area of a largest square fit in a right angle triangle

• Last Updated : 22 Jun, 2022

Given a right angled triangle with height l, base b & hypotenuse h.We need to find the area of the largest square that can fit in the right angled triangle.

Examples:

```Input: l = 3, b = 4, h = 5
Output: 2.93878
The biggest square that can fit inside
is of 1.71428 * 1.71428 dimension

Input: l = 5, b = 12, h = 13
Output: 12.4567```

Considering the above diagram, we see,tanx = l/b
Here it is also true that, tanx = a/(b-a)
So, l/b = a/(b-a) which means that, a = (l*b)/(l+b)

Below is the required implementation:

## C++

 `// C++ Program to find the area of the biggest square``// which can fit inside the right angled triangle``#include ``using` `namespace` `std;` `// Function to find the area of the biggest square``float` `squareArea(``float` `l, ``float` `b, ``float` `h)``{` `    ``// the height or base or hypotenuse``    ``// cannot be negative``    ``if` `(l < 0 || b < 0 || h < 0)``        ``return` `-1;` `    ``// side of the square``    ``float` `a = (l * b) / (l + b);` `    ``// squaring to get the area``    ``return` `a * a;``}` `// Driver code``int` `main()``{``    ``float` `l = 5, b = 12, h = 13;``    ``cout << squareArea(l, b, h) << endl;` `    ``return` `0;``}`

## Java

 `//Java Program to find the area of the biggest square``//which can fit inside the right angled triangle``public` `class` `GFG {` `    ``//Function to find the area of the biggest square``    ``static` `float` `squareArea(``float` `l, ``float` `b, ``float` `h)``    ``{` `     ``// the height or base or hypotenuse``     ``// cannot be negative``     ``if` `(l < ``0` `|| b < ``0` `|| h < ``0``)``         ``return` `-``1``;` `     ``// side of the square``     ``float` `a = (l * b) / (l + b);` `     ``// squaring to get the area``     ``return` `a * a;``    ``}` `    ``//Driver code``    ``public` `static` `void` `main(String[] args) {``        ` `         ``float` `l = ``5``, b = ``12``, h = ``13``;``         ``System.out.println(squareArea(l, b, h));``    ``}``}`

## Python3

 `# Python 3 Program  to find the``# area of the biggest square``# which can fit inside the right``# angled triangle` `# Function to find the area of the biggest square``def` `squareArea(l, b, h) :` `    ``# the height or base or hypotenuse``    ``# cannot be negative``    ``if` `l < ``0` `or` `b < ``0` `or` `h < ``0` `:``        ``return` `-``1` `    ``# side of the square``    ``a ``=` `(l ``*` `b) ``/` `(l ``+` `b)` `    ``# squaring to get the area``    ``return` `a ``*` `a` `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:` `    ``l, b, h ``=` `5``, ``12``, ``13` `    ``print``(``round``(squareArea(l, b, h),``4``))` `# This code is contributed by ANKITRAI1`

## C#

 `// C# Program to find the area of``// the biggest square which can``// fit inside the right angled triangle``using` `System;``class` `GFG``{` `// Function to find the area``// of the biggest square``static` `float` `squareArea(``float` `l, ``float` `b,``                        ``float` `h)``{` `// the height or base or hypotenuse``// cannot be negative``if` `(l < 0 || b < 0 || h < 0)``    ``return` `-1;` `// side of the square``float` `a = (l * b) / (l + b);` `// squaring to get the area``return` `a * a;``}` `// Driver code``public` `static` `void` `Main()``{``    ``float` `l = 5, b = 12, h = 13;``    ``Console.WriteLine(squareArea(l, b, h));``}``}` `// This code is contributed``// by inder_verma..`

## PHP

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## Javascript

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Output:

`12.4567`

Time complexity: O(1)

space complexity: O(1)

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