# Find other two sides of a right angle triangle

Given one side of right angle triangle, check if there exists a right angle triangle possible with any other two sides of the triangle. If possible print length of the other two sides.

Else print -1

Note: All the sides of triangle must be positive integers

**Example 1:**

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Input :a = 3Output :b = 4, c = 5Explanation :a = 3, b = 4 and c = 5 form right angle triangle because 3^{2}+ 4^{2}= 9 + 16 = 25 = 5^{2}=> 3^{2}+ 4^{2}= 5^{2}

**Example 2:**

Input :a = 11Output :b = 60, c = 61Explanation :a = 11, b = 60 and c = 61 form right angle triangle because 11^{2}+ 60^{2}= 121 + 3600 = 3721 = 61^{2}=> 11^{2}+ 60^{2}= 61^{2}

To solve this problem we first observe the Pythagoras equation. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:

a^{2}+ b^{2}= c^{2}

**Case 1 – a is an odd number:**Given a, find b and c

c^{2}- b^{2}= a^{2}OR c = (a^{2}+ 1)/2; b = (a^{2}- 1)/2;

- Above solution works only for case when a is odd, because a
^{2}+ 1 is divisible by 2 only for odd a. **Case 2 – a is an even number:**When c-b is 2 & c+b is (a^{2})/2

c-b = 2 & c+b = (a^{2})/2 Hence, c = (a^{2})/4 + 1; b = (a^{2})/4 - 1;

This works when a is even.

This solution doesn’t work for case of a = 1 and a = 2 because there isn’t any right angle triangle with side 1 or 2 with all integer sides.

## C++

`// C++ program to print other two sides of right` `// angle triangle given one side` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Finds two sides of a right angle triangle` `// if it exist.` `void` `printOtherSides(` `int` `n)` `{` ` ` `// if n is odd` ` ` `if` `(n & 1)` ` ` `{` ` ` `// case of n = 1 handled separately` ` ` `if` `(n == 1)` ` ` `cout << -1 << endl;` ` ` `else` ` ` `{` ` ` `int` `b = (n*n-1)/2;` ` ` `int` `c = (n*n+1)/2;` ` ` `cout << ` `"b = "` `<< b` ` ` `<< ` `", c = "` `<< c << endl;` ` ` `}` ` ` `}` ` ` `else` ` ` `{` ` ` `// case of n = 2 handled separately` ` ` `if` `(n == 2)` ` ` `cout << -1 << endl;` ` ` `else` ` ` `{` ` ` `int` `b = n*n/4-1;` ` ` `int` `c = n*n/4+1;` ` ` `cout << ` `"b = "` `<< b` ` ` `<< ` `", c = "` `<< c << endl;` ` ` `}` ` ` `}` `}` `// Driver program to test above function` `int` `main()` `{` ` ` `int` `a = 3;` ` ` `printOtherSides(a);` ` ` `return` `0;` `}` |

## Java

`// Java program to print other two` `// sides of right angle triangle` `// given one side` `class` `GFG` `{` ` ` `// Finds two sides of a right angle` ` ` `// triangle if it they exist.` ` ` `static` `void` `printOtherSides(` `int` `n)` ` ` `{` ` ` `// if n is odd` ` ` `if` `(n % ` `2` `!= ` `0` `)` ` ` `{` ` ` `// case of n = 1 handled separately` ` ` `if` `(n == ` `1` `)` ` ` `System.out.println(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `int` `b = (n * n -` `1` `) / ` `2` `;` ` ` `int` `c = (n *n +` `1` `) / ` `2` `;` ` ` `System.out.println(` `"b = "` `+ b +` ` ` `", c = "` `+c);` ` ` `}` ` ` `}` ` ` `else` ` ` `{` ` ` `// case of n = 2 handled separately` ` ` `if` `(n == ` `2` `)` ` ` `System.out.println(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `int` `b = n * n / ` `4` `- ` `1` `;` ` ` `int` `c = n * n / ` `4` `+ ` `1` `;` ` ` `System.out.println(` `"b = "` `+ b +` ` ` `", c = "` `+c);` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `a = ` `3` `;` ` ` `printOtherSides(a);` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python

`# Python program to print other` `# two sides of right angle` `# triangle given one side` `# Finds two sides of a right angle` `# triangle if it they exist.` `def` `printOtherSides(n):` ` ` ` ` `# if n is odd` ` ` `if` `(n & ` `1` `):` ` ` ` ` `# case of n = 1 handled` ` ` `# separately` ` ` `if` `(n ` `=` `=` `1` `):` ` ` `print` `(` `-` `1` `)` ` ` `else` `:` ` ` `b ` `=` `(n ` `*` `n ` `-` `1` `) ` `/` `/` `2` ` ` `c ` `=` `(n ` `*` `n ` `+` `1` `) ` `/` `/` `2` ` ` `print` `(` `"b ="` `, b, ` `", c ="` `, c)` ` ` `else` `:` ` ` ` ` `# case of n = 2 handled` ` ` `# separately` ` ` `if` `(n ` `=` `=` `2` `):` ` ` `print` `(` `-` `1` `)` ` ` `else` `:` ` ` `b ` `=` `n ` `*` `n ` `/` `/` `4` `-` `1` ` ` `c ` `=` `n ` `*` `n ` `/` `/` `4` `+` `1` ` ` `print` `(` `"b ="` `, b` `", c ="` `, c)` `# Driver Code` `a ` `=` `3` `printOtherSides(a)` `# This code is contributed by` `# Sanjit_Prasad` |

## C#

`// C# program to print other two` `// sides of right angle triangle` `// given one side` `using` `System;` `class` `GFG {` ` ` ` ` `// Finds two sides of a right angle` ` ` `// triangle if it they exist.` ` ` `static` `void` `printOtherSides(` `int` `n)` ` ` `{` ` ` ` ` `// if n is odd` ` ` `if` `(n % 2 != 0)` ` ` `{` ` ` ` ` `// case of n = 1 handled` ` ` `// separately` ` ` `if` `(n == 1)` ` ` `Console.WriteLine(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `int` `b = (n * n - 1) / 2;` ` ` `int` `c = (n * n + 1) / 2;` ` ` `Console.Write(` `"b = "` `+ b +` ` ` `", c = "` `+ c);` ` ` `}` ` ` `}` ` ` `else` ` ` `{` ` ` ` ` `// case of n = 2 handled` ` ` `// separately` ` ` `if` `(n == 2)` ` ` `Console.Write(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `int` `b = n * n / 4 - 1;` ` ` `int` `c = n * n / 4 + 1;` ` ` `Console.Write(` `"b = "` `+ b +` ` ` `", c = "` `+ c);` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `a = 3;` ` ` `printOtherSides(a);` ` ` `}` `}` `// This code is contributed by Nitin Mittal.` |

## PHP

`<?php` `// PHP program to print other two` `// sides of right angle triangle` `// given one side` `// Finds two sides of a right angle` `// triangle if it they exist.` `function` `printOtherSides(` `$n` `)` `{` ` ` ` ` `// if n is odd` ` ` `if` `(` `$n` `& 1)` ` ` `{` ` ` `// case of n = 1` ` ` `// handled separately` ` ` `if` `(` `$n` `== 1)` ` ` `echo` `-1 ;` ` ` `else` ` ` `{` ` ` `$b` `= (` `$n` `* ` `$n` `- 1) / 2;` ` ` `$c` `= (` `$n` `* ` `$n` `+ 1) / 2;` ` ` `echo` `"b = "` `,` `$b` `,` `", c = "` `,` `$c` `;` ` ` `}` ` ` `}` ` ` `else` ` ` `{` ` ` ` ` `// case of n = 2` ` ` `// handled separately` ` ` `if` `(` `$n` `== 2)` ` ` `echo` `-1 ;` ` ` `else` ` ` `{` ` ` `$b` `= ` `$n` `* ` `$n` `/ 4 - 1;` ` ` `$c` `= ` `$n` `* ` `$n` `/ 4 + 1;` ` ` `echo` `"b = "` `,` `$b` `, ` `", c = "` `, ` `$c` `;` ` ` `}` ` ` `}` `}` ` ` `// Driver Code` ` ` `$a` `= 3;` ` ` `printOtherSides(` `$a` `);` ` ` `return` `0;` `// This code is contributed by nitin mittal.` `?>` |

## Javascript

`<script>` `// javascript program to print other two` `// sides of right angle triangle` `// given one side ` `// Finds two sides of a right angle` `// triangle if it they exist.` `function` `printOtherSides(n)` `{` ` ` `// if n is odd` ` ` `if` `(n % 2 != 0)` ` ` `{` ` ` `// case of n = 1 handled separately` ` ` `if` `(n == 1)` ` ` `document.write(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `var` `b = (n * n -1) / 2;` ` ` `var` `c = (n *n +1) / 2;` ` ` `document.write(` `"b = "` `+ b +` ` ` `", c = "` `+c);` ` ` `}` ` ` `}` ` ` `else` ` ` `{` ` ` `// case of n = 2 handled separately` ` ` `if` `(n == 2)` ` ` `document.write(` `"-1"` `);` ` ` `else` ` ` `{` ` ` `var` `b = n * n / 4 - 1;` ` ` `var` `c = n * n / 4 + 1;` ` ` `document.write(` `"b = "` `+ b +` ` ` `", c = "` `+c);` ` ` `}` ` ` `}` `}` ` ` `// Driver code` `var` `a = 3;` `printOtherSides(a);` `// This code is contributed by 29AjayKumar` `</script>` |

Output:

b = 4, c = 5

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