# Minimum and maximum possible length of the third side of a triangle

• Last Updated : 25 Mar, 2021

Given two sides of a triangle s1 and s2, the task is to find the minimum and maximum possible length of the third side of the given triangle. Print -1 if it is not possible to make a triangle with the given side lengths. Note that the length of all the sides must be integers.
Examples:

Input: s1 = 3, s2 = 6
Output:
Max = 8
Min = 4
Input: s1 = 5, s2 = 8
Output:
Max = 12
Min = 4

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Approach: Let s1, s2 and s3 be the sides of the given triangle where s1 and s2 are given. As we know that in a triangle, the sum of two sides must always be greater than the third side. So, the following equations must be satisfied:

1. s1 + s2 > s3
2. s1 + s3 > s2
3. s2 + s3 > s1

Solving for s3, we get s3 < s1 + s2, s3 > s2 – s1 and s3 > s1 – s2
It is clear now that the length of the third side must lie in the range (max(s1, s2) – min(s1, s2), s1 + s2)
So, the minimum possible value will be max(s1, s2) – min(s1, s2) + 1 and the maximum possible value will be s1 + s2 – 1.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to find the minimum and the``// maximum possible length of the third``// side of the given triangle``void` `find_length(``int` `s1, ``int` `s2)``{` `    ``// Not a valid triangle``    ``if` `(s1 <= 0 || s2 <= 0) {``        ``cout << -1;``        ``return``;``    ``}``    ``int` `max_length = s1 + s2 - 1;``    ``int` `min_length = max(s1, s2) - min(s1, s2) + 1;` `    ``// Not a valid triangle``    ``if` `(min_length > max_length) {``        ``cout << -1;``        ``return``;``    ``}` `    ``cout << ``"Max = "` `<< max_length << endl;``    ``cout << ``"Min = "` `<< min_length;``}` `// Driver code``int` `main()``{``    ``int` `s1 = 8, s2 = 5;``    ``find_length(s1, s2);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.io.*;` `class` `GFG``{` `// Function to find the minimum and the``// maximum possible length of the third``// side of the given triangle``static` `void` `find_length(``int` `s1, ``int` `s2)``{` `    ``// Not a valid triangle``    ``if` `(s1 <= ``0` `|| s2 <= ``0``)``    ``{``        ``System.out.print(-``1``);``        ``return``;``    ``}``    ``int` `max_length = s1 + s2 - ``1``;``    ``int` `min_length = Math.max(s1, s2) - Math.min(s1, s2) + ``1``;` `    ``// Not a valid triangle``    ``if` `(min_length > max_length)``    ``{``        ``System.out.print(-``1``);``        ``return``;``    ``}` `    ``System.out.println(``"Max = "` `+ max_length);``    ``System.out.print(``"Min = "` `+ min_length);``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `s1 = ``8``, s2 = ``5``;``    ``find_length(s1, s2);``}``}` `// This code is contributed by anuj_67..`

## Python3

 `# Python3 implementation of the approach` `# Function to find the minimum and the``# maximum possible length of the third``# side of the given triangle``def` `find_length(s1, s2) :` `    ``# Not a valid triangle``    ``if` `(s1 <``=` `0` `or` `s2 <``=` `0``) :``        ``print``(``-``1``, end ``=` `"");``        ``return``;``        ` `    ``max_length ``=` `s1 ``+` `s2 ``-` `1``;``    ``min_length ``=` `max``(s1, s2) ``-` `min``(s1, s2) ``+` `1``;` `    ``# Not a valid triangle``    ``if` `(min_length > max_length) :``        ``print``(``-``1``, end ``=` `"");``        ``return``;` `    ``print``(``"Max ="``, max_length);``    ``print``(``"Min ="``, min_length);`  `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``s1 ``=` `8``;``    ``s2 ``=` `5``;``    ` `    ``find_length(s1, s2);``    ` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to find the minimum and the``// maximum possible length of the third``// side of the given triangle``static` `void` `find_length(``int` `s1, ``int` `s2)``{` `    ``// Not a valid triangle``    ``if` `(s1 <= 0 || s2 <= 0)``    ``{``        ``Console.Write(-1);``        ``return``;``    ``}``    ``int` `max_length = s1 + s2 - 1;``    ``int` `min_length = Math.Max(s1, s2) - Math.Min(s1, s2) + 1;` `    ``// Not a valid triangle``    ``if` `(min_length > max_length)``    ``{``        ``Console.WriteLine(-1);``        ``return``;``    ``}` `    ``Console.WriteLine(``"Max = "` `+ max_length);``    ``Console.WriteLine(``"Min = "` `+ min_length);``}` `// Driver code``public` `static` `void` `Main ()``{``    ``int` `s1 = 8, s2 = 5;``    ``find_length(s1, s2);``}``}` `// This code is contributed by anuj_67..`

## Javascript

 ``
Output:
```Max = 12
Min = 4```

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