Java Min Perimeter Rectangle
public class Solution {
    public static int minPerimeterRectangle(int n) {
        long i = 1;
        long min = Long.MAX_VALUE;

        while (i * i < n) {
            if (n % i == 0) {
                min = Math.min(min, 2 * (i + n / i));
            }
            i++;
        }

        return (int) min;
    }
}

This searches factor pairs up to the square root and picks the pair with the smallest perimeter.