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++ 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 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) |
<?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 ?> |
<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> |
Maximum Area = 90
Time Complexity: O(1)
Auxiliary Space: O(1)