Sum of perimeter of all the squares in a rectangle using JavaScript

Problem: Suppose there are 5 squares embedded inside a rectangle like this −

The squares follow a Fibonacci-like pattern where each square's side length equals the sum of the two preceding squares. Their perimeter will be −

4 + 4 + 8 + 12 + 20 = 48 units

We are required to write a JavaScript function that takes in a number n and returns the sum of the perimeter if there are n squares embedded.

How It Works

The algorithm generates a Fibonacci sequence for square side lengths, then calculates the total perimeter:

1. Start with two squares of side length 1
2. Each subsequent square has side length = sum of previous two squares
3. Calculate perimeter for each square (side × 4)
4. Sum all perimeters

Example

Following is the code −

const num = 6;
const findPerimeter = (num = 1) => {
    const arr = [1, 1];
    let n = 0;
    let sum = 2;
    for(let i = 0; i < num - 1; i++){
        n = arr[i] + arr[i + 1];
        arr.push(n);
        sum += n;
    }
    return sum * 4;
};
console.log(findPerimeter(num - 1));

Output

80

Step-by-Step Breakdown

const findPerimeterDetailed = (num = 1) => {
    const sides = [1, 1];  // First two squares have side 1
    console.log("Square sides:", sides);
    
    // Generate remaining square sides using Fibonacci pattern
    for(let i = 0; i < num - 1; i++){
        let nextSide = sides[i] + sides[i + 1];
        sides.push(nextSide);
        console.log(`Square ${i + 3}: side = ${nextSide}`);
    }
    
    // Calculate total perimeter
    let totalPerimeter = 0;
    sides.forEach((side, index) => {
        let perimeter = side * 4;
        totalPerimeter += perimeter;
        console.log(`Square ${index + 1}: perimeter = ${perimeter}`);
    });
    
    return totalPerimeter;
};

console.log("Final result:", findPerimeterDetailed(4));

Output

Square sides: [ 1, 1 ]
Square 3: side = 2
Square 4: side = 3
Square 5: side = 5
Square 1: perimeter = 4
Square 2: perimeter = 4
Square 3: perimeter = 8
Square 4: perimeter = 12
Square 5: perimeter = 20
Final result: 48

Conclusion

This solution efficiently calculates the sum of perimeters using the Fibonacci sequence pattern. The key insight is that square sides follow Fibonacci numbers, and the total perimeter is 4 times the sum of all side lengths.