Maximum area of rectangle possible with given perimeter

Given the perimeter of a rectangle, the task is to find the maximum area of a rectangle which can use n-unit length as its perimeter.
Note: Length and Breadth must be an integral value.

Example:

```Input: perimeter = 15
Output: Maximum Area = 12

Input: perimeter = 16
Output: Maximum Area = 16
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).

Below is the implementation of the above approach:

 `// CPP to find maximum area rectangle ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find max area ` `int` `maxArea(``float` `perimeter) ` `{ ` `    ``int` `length = (``int``)``ceil``(perimeter / 4); ` `    ``int` `breadth = (``int``)``floor``(perimeter / 4); ` ` `  `    ``// return area ` `    ``return` `length * breadth; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``float` `n = 38; ` `    ``cout << ``"Maximum Area = "` `<< maxArea(n); ` ` `  `    ``return` `0; ` `} `

 `//Java to find maximum area rectangle ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `// Function to find max area ` `static` `int` `maxArea(``float` `perimeter) ` `{ ` `    ``int` `length = (``int``)Math.ceil(perimeter / ``4``); ` `    ``int` `breadth = (``int``)Math.floor(perimeter / ``4``); ` ` `  `// return area ` `return` `length * breadth; ` `} ` ` `  `// Driver code ` `     `  `    ``public` `static` `void` `main (String[] args) { ` ` `  `        ``float` `n = ``38``; ` `        ``System.out.println(``"Maximum Area = "` `+ ` `                ``maxArea(n)); ` `         `  `    ``} ` `} `

 `# Python3 program to find ` `# maximum area rectangle ` `from` `math ``import` `ceil, floor ` ` `  `# Function to find max area ` `def` `maxArea(perimeter): ` `    ``length ``=` `int``(ceil(perimeter ``/` `4``)) ` `    ``breadth ``=` `int``(floor(perimeter ``/` `4``)) ` ` `  `    ``# return area ` `    ``return` `length ``*` `breadth ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `38` `    ``print``(``"Maximum Area ="``, maxArea(n)) `

 `// C# to find maximum area rectangle ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// Function to find max area ` `static` `int` `maxArea(``float` `perimeter) ` `{ ` `    ``int` `length = (``int``)Math.Ceiling(perimeter / 4); ` `    ``int` `breadth = (``int``)Math.Floor(perimeter / 4); ` ` `  `    ``// return area ` `    ``return` `length * breadth; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``float` `n = 38; ` `    ``Console.WriteLine(``"Maximum Area = "` `+  ` `                             ``maxArea(n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by Akanksha Rai(Abby_akku) `

 ` `

Output:
```Maximum Area = 90
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :