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 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++

// C++ 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;
}

Java

//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

# 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#

// 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)

PHP

<?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
?>

Javascript

<script>

// JavaScript to find maximum area rectangle

// Function to find max area
function maxArea(perimeter)
{
    let length = Math.ceil(perimeter / 4);
    let breadth = Math.floor(perimeter / 4);

    // return area
    return length * breadth;
}

// Driver code
let n = 38;

document.write("Maximum Area = " + maxArea(n));

// This code is contributed by Manoj.

</script>

Output:

Maximum Area = 90

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