# Find the length of the median of a Triangle if length of sides are given

Given the length of all three sides of a triangle as **a**, **b** and **c**. The task is to calculate the length of the median of the triangle.

A

median of a triangleis a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.

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**Examples:**

Input:a = 8, b = 10, c = 13Output:10.89Input:a = 4, b = 3, c = 5Output:3.61

**Approach:** The idea is to use Apollonius’s theorem to solve this problem.

Apollonius’s Theoremstates that “the sum of the squares of any two sides of a triangle equals twice the square on half the third side and twice the square on the median bisecting the third side”.

From the above figure, According to Apollonius’s Theorem we have:

where a, b, and c are the length of sides of the triangle

and m is the length of median of the triangle on side 2*a

Therefore, the length of the median of a triangle from the above equation is given by:

Below is the implementation of the above approach:

## C++

`// C++ program to find the length of the` `// median using sides of the triangle` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the length of` `// the median using sides of triangle` `float` `median(` `int` `a, ` `int` `b, ` `int` `c)` `{` ` ` `float` `n = ` `sqrt` `(2 * b * b +` ` ` `2 * c * c - a * a) / 2;` ` ` `return` `n;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a, b, c;` ` ` `a = 4;` ` ` `b = 3;` ` ` `c = 5;` ` ` `// Function call` ` ` `float` `ans = median(a, b, c);` ` ` `// Print final answer with 2` ` ` `// digits after decimal` ` ` `cout << fixed << setprecision(2) << ans;` ` ` `return` `0;` `}` `// This code is contributed by himanshu77` |

## Java

`// Java program to find the length of the` `// median using sides of the triangle` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to return the length of` `// the median using sides of triangle` `public` `static` `float` `median(` `int` `a, ` `int` `b, ` `int` `c)` `{` ` ` `float` `n = (` `float` `)(Math.sqrt(` `2` `* b * b +` ` ` `2` `* c * c -` ` ` `a * a) / ` `2` `);` ` ` `return` `n;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `a, b, c;` ` ` `a = ` `4` `;` ` ` `b = ` `3` `;` ` ` `c = ` `5` `;` ` ` `// Function call` ` ` `float` `ans = median(a, b, c);` ` ` `// Print final answer with 2` ` ` `// digits after decimal` ` ` `System.out.println(String.format(` `"%.2f"` `, ans));` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Python3

`# Python3 implementation to Find the` `# length of the median using sides` `# of the triangle` `import` `math` `# Function to return the length of` `# the median using sides of triangle.` `def` `median(a, b, c):` ` ` ` ` `n ` `=` `(` `1` `/` `2` `)` `*` `math.sqrt(` `2` `*` `(b` `*` `*` `2` `)` ` ` `+` `2` `*` `(c` `*` `*` `2` `)` ` ` `-` `a` `*` `*` `2` `) ` ` ` `return` `n` `# Driver Code` `a ` `=` `4` `b ` `=` `3` `c ` `=` `5` `# Function Call` `ans ` `=` `median(a, b, c)` `# Print the final answer` `print` `(` `round` `(ans, ` `2` `))` |

## C#

`// C# program to find the length of the` `// median using sides of the triangle` `using` `System;` `class` `GFG{` ` ` `// Function to return the length of` `// the median using sides of triangle` `public` `static` `float` `median(` `int` `a, ` `int` `b, ` `int` `c)` `{` ` ` `float` `n = (` `float` `)(Math.Sqrt(2 * b * b +` ` ` `2 * c * c -` ` ` `a * a) / 2);` ` ` `return` `n;` `}` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `a, b, c;` ` ` `a = 4;` ` ` `b = 3;` ` ` `c = 5;` ` ` `// Function call` ` ` `float` `ans = median(a, b, c);` ` ` `// Print readonly answer with 2` ` ` `// digits after decimal` ` ` `Console.WriteLine(String.Format(` `"{0:F2}"` `, ans));` `}` `}` `// This code is contributed by gauravrajput1` |

## Javascript

`<script>` `// JavaScript program to find the length of the` `// median using sides of the triangle` `// Function to return the length of` `// the median using sides of triangle` `function` `median(a, b, c)` `{` ` ` `let n = (Math.sqrt(2 * b * b +` ` ` `2 * c * c -` ` ` `a * a) / 2);` ` ` `return` `n;` `}` ` ` `// Driver Code` ` ` `let a, b, c;` ` ` `a = 4;` ` ` `b = 3;` ` ` `c = 5;` ` ` ` ` `// Function call` ` ` `let ans = median(a, b, c);` ` ` ` ` `// Print final answer with 2` ` ` `// digits after decimal` ` ` `document.write(ans, 2);` ` ` `</script>` |

**Output:**

3.61

**Time Complexity: **O(1) **Space Complexity: **O(1)