Find the percentage change in the area of a Rectangle

Given two integers P and Q which represents the percentage change in the length and breadth of the rectangle, the task is to print the percentage change in the area of the rectangle.

Examples:

Input: P = 10, Q = 20
Output: 32
Explanation:
Let the initial length of the rectangle be 100 and breadth be 80.
Initial area = 8000.
New length = 110 and new breadth = 96. Therefore, the new area = 10560.
The percentage change in the area = ((10560 – 8000) / 8000) * 100 = 32.



Input: P = 20, Q = -10
Output: 8
Let initial length of the rectangle be 100 and breadth be 80.
Initial area = 8000.
New length = 120 and new breadth = 72. Therefore, new area = 8640.
The percentage change in the area = ((8640 – 8000) / 8000) * 100 = 8.

Approach:

  • Since the area of the rectangle is given by the formula:
    area = length * breadth
    
  • Let the initial length of the rectangle be L and the breadth of the rectangle be B. Therefore, the initial area is given by L * B.
  • Therefore, the new length and breadth are given as:
    L' = L + ((P/100)*L)
    B' = B + ((Q/100)*B)
    
  • Therefore, the new length and breadth are given as:

    new area = [L + ((C/100)*L)] * [B + ( ( D / 100) * B)]

  • The percentage change in the area is given by the formula:


    % change = ((new area – old area) / old area )*100

  • Below is the implementation of the above approach:

    C++

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    // CPP implementation to find the percentage
    #include <bits/stdc++.h>
    using namespace std;
      
    // change in the area when the percentage change
    // in the length and breadth is given
      
    // Function to calculate percentage
    // change in area of rectangle
    int calculate_change(int length, int breadth){
        int change = 0;
        change = length + breadth+((length * breadth)/100);
        return change;
      }
      
    // Driver code
    int main()
    {
      int cL = 20;
      int cB = -10;
      int cA = calculate_change(cL, cB);
      
      printf("%d",cA);
      return 0;
    }

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    Java

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    // Java implementation to find the percentage
    import java.util.*;
      
    class GFG{
      
        // change in the area when the percentage change
        // in the length and breadth is given
      
        // Function to calculate percentage
        // change in area of rectangle
        static int calculate_change(int length, int breadth){
            int change = 0;
            change = length + breadth+((length * breadth)/100);
            return change;
        }
          
        // Driver code
        public static void main(String args[])
        {
            int cL = 20;
            int cB = -10;
            int cA = calculate_change(cL, cB);
              
            System.out.println(+ cA);
          
        }
    }
      
    // This code is contributed by AbhiThakur
      

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    Python3

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    # Python3 implementation to find the percentage
    # change in the area when the percentage change
    # in the length and breadth is given
      
    # Function to calculate percentage 
    # change in area of rectangle
    def calculate_change(length, breadth):
        change = 0
        change = length + breadth+((length * breadth)//100)
        return change
      
    # Driver code
    if __name__ == "__main__":
        cL = 20
        cB = -10
        cA = calculate_change(cL, cB)
      
        print(cA)
      
    # This code is contributed by mohit kumar 29

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    C#

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    // C# implementation to find the percentage
    using System;
    using System.Collections.Generic;
    using System.Linq;
      
    class GFG 
    {
          
    // change in the area when the percentage change
    // in the length and breadth is given
      
    // Function to calculate percentage
    // change in area of rectangle
    static int calculate_change(int length, int breadth){
        int change = 0;
        change = length + breadth + ((length * breadth)/100);
        return change;
    }
      
    // Driver Code
    public static void Main(String[] args) 
    {
        int cL = 20;
        int cB = -10;
        int cA = calculate_change(cL, cB);
          
        Console.Write(cA);
    }
    }
      
    // This code is contributed by shivanisinghss2110

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    Output:

    8
    

    Time Complexity: O(1)

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