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


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:

C++

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// CPP to find maximum area rectangle
#include <bits/stdc++.h>
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;
}

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Java

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//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));
          
    }
}

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Python3

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# 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))

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C#

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// 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)

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PHP

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<?php
// PHP to find maximum area rectangle 
  
// Function to find max area 
function maxArea($perimeter
    $length = (int)ceil($perimeter / 4); 
    $breadth = (int)floor($perimeter / 4); 
  
    // return area 
    return ($length * $breadth); 
  
// Driver code 
$n = 38; 
echo "Maximum Area = " , maxArea($n); 
  
// This code is contributed by jit_t
?>

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Output:

Maximum Area = 90


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