# Length of longest rod that can fit into a cuboid

Given the length, breadth, and height of a cuboid, the task is to find the length of the longest rod that can fit in a cuboid.

Examples:

Input: length = 12, breadth = 9, height = 8
Output: 17

Input: length = 22, breadth = 19, height = 8
Output: 30.1496

Explanation: In the figure

`GH = length, GF = breadth, FB= height`

The length of the longest rod is BH. Therefore to compute BH we can apply Pythagoras Theorem in Triangle BHF. From triangle HGF we can compute the length of FH.

After getting the length of FH we can find the length of BH using Pythagoras theorem in triangle BHF.

Follow the below steps to implement the above idea:

• Declare a double variable named result to hold the length of the longest rod.
• Declare an integer variable named temp to hold the intermediate result.
• Calculate the intermediate result by adding the square of the length, breadth, and height values.
• Calculate the length of the longest rod by finding the square root of the intermediate result, and assign it to the result variable.
• Return the value of result.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the longest rod``// that can fit in a cuboid``#include ``using` `namespace` `std;` `// Function to find the length``double` `longestRodInCuboid(``int` `length, ``                        ``int` `breadth, ``int` `height)``{``    ``double` `result;``    ``int` `temp;` `    ``// temporary variable to hold``    ``// the intermediate result``    ``temp = length * length + breadth * breadth ``           ``+ height * height;` `    ``// length of longest rod is calculated``    ``// using square root function``    ``result = ``sqrt``(temp);` `    ``return` `result;``}` `// Driver code``int` `main()``{``    ``int` `length = 12, breadth = 9, height = 8;` `    ``// calling longestRodInCuboid() function to``    ``// get the length of longest rod``    ``cout << longestRodInCuboid(length, breadth, height);` `    ``return` `0;``}`

## Java

 `// Java program to find the longest``// rod that can fit in a cuboid``class` `GFG ``{` `// Function to find the length``static` `double` `longestRodInCuboid(``int` `length, ``                                 ``int` `breadth, ``                                 ``int` `height)``{``    ``double` `result;``    ``int` `temp;``    ` `    ``// temporary variable to hold``    ``// the intermediate result``    ``temp = length * length + breadth * ``           ``breadth + height * height;``    ` `    ``// length of longest rod is calculated``    ``// using square root function``    ``result = Math.sqrt(temp);``    ` `    ``return` `result;``}` `// Driver Code``public` `static` `void` `main(String[] args) ``{``    ``int` `length = ``12``, ``        ``breadth = ``9``,``        ``height = ``8``;` `    ``// calling longestRodInCuboid() ``    ``// function to get the length ``    ``// of longest rod``    ``System.out.println((``int``)longestRodInCuboid(length,``                                    ``breadth, height));``}``}` `// This code is contributed by ChitraNayal`

## Python 3

 `# Python 3 program to find the longest rod ``# that can fit in a cuboid` `# from math lib. import everything``from` `math ``import` `*` `# Function to find the length ``def` `longestRodInCuboid(length, breadth, height) :` `    ``# temporary variable to hold ``    ``# the intermediate result``    ``temp ``=` `length ``*` `length ``+` `breadth  ``*` `breadth ``+` `height ``*` `height` `    ``#  length of longest rod is calculated ``    ``# using square root function``    ``result ``=` `sqrt(temp)` `    ``return` `result`  `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:` `    ``length, breadth, height ``=` `12``, ``9``, ``8` `    ``# calling longestRodInCuboid() function to ``    ``# get the length of longest rod``    ``print``(longestRodInCuboid(length, breadth, height))`  `# This code is contributed by ANKITRAI1`

## C#

 `// C# program to find the longest``// rod that can fit in a cuboid``using` `System;``class` `GFG ``{` `// Function to find the length``static` `double` `longestRodInCuboid(``int` `length, ``                                ``int` `breadth, ``                                ``int` `height)``{``    ``double` `result;``    ``int` `temp;``    ` `    ``// temporary variable to hold``    ``// the intermediate result``    ``temp = length * length + breadth * ``        ``breadth + height * height;``    ` `    ``// length of longest rod is calculated``    ``// using square root function``    ``result = Math.Sqrt(temp);``    ` `    ``return` `result;``}` `// Driver Code``public` `static` `void` `Main() ``{``    ``int` `length = 12, ``        ``breadth = 9,``        ``height = 8;` `    ``// calling longestRodInCuboid() ``    ``// function to get the length ``    ``// of longest rod``    ``Console.WriteLine((``int``)longestRodInCuboid(length,``                                    ``breadth, height));``}``}` `// This code is contributed by inder_verma..`

## PHP

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## Javascript

 ``

Output:
`17`

Time Complexity: O(log n), as the inbuilt sqrt function takes logarithmic time
Auxiliary Space: O(1)

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