Area of a largest square fit in a right angle triangle

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 traingle` `#include <bits/stdc++.h>` `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 traingle` `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));` ` ` `}` `}` |

## Python 3

`# Python 3 Program to find the` `# area of the biggest square` `# which can fit inside the right` `# angled traingle` `# 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

`<?php` `// PHP 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` `function` `squareArea(` `$l` `, ` `$b` `, ` `$h` `)` `{` ` ` `// the height or base or` ` ` `// hypotenuse cannot be` ` ` `// negative` ` ` `if` `(` `$l` `< 0 || ` `$b` `< 0 || ` `$h` `< 0)` ` ` `return` `-1;` ` ` `// side of the square` ` ` `$a` `= (` `$l` `* ` `$b` `) / (` `$l` `+ ` `$b` `);` ` ` `// squaring to get the area` ` ` `return` `$a` `* ` `$a` `;` `}` `// Driver code` `$l` `= 5;` `$b` `= 12;` `$h` `= 13;` `echo` `round` `(squareArea(` `$l` `, ` `$b` `, ` `$h` `), 4);` `// This code is contributed by mits` `?>` |

## Javascript

`<script>` `// javascript Program to find the area of the biggest square` `// which can fit inside the right angled traingle` `// Function to find the area of the biggest square` `function` `squareArea(l , b , h)` `{` ` ` `// the height or base or hypotenuse` ` ` `// cannot be negative` ` ` `if` `(l < 0 || b < 0 || h < 0)` ` ` `return` `-1;` ` ` `// side of the square` ` ` `var` `a = (l * b) / (l + b);` ` ` `// squaring to get the area` ` ` `return` `a * a;` `}` `// Driver code` ` ` ` ` `var` `l = 5, b = 12, h = 13;` ` ` `document.write(squareArea(l, b, h).toFixed(4));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

12.4567

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