My code

… was written in C++ and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <cmath>
       
 
       
int main()
       
{
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    unsigned int target = 2000000;
       
    std::cin >> target;
       
 
       
    // assume x <= y, therefore x <= sqrt(limit)
       
    unsigned int root = sqrt(target);
       
    unsigned int bestRectangles = 0;
       
    unsigned int bestArea       = 0;
       
    for (unsigned int x = 1; x <= root + 1; x++) // allow slight overshooting
       
    {
       
      // start with a sqaure
       
      unsigned int y = x;
       
      // number of rectangles
       
      unsigned int rectangles = 0;
       
 
       
      // slowly increase y until too many rectangle in the grid
       
      do
       
      {
       
        unsigned int area = x * y;
       
 
       
        // the formula derived above
       
        rectangles = x * (x + 1) * y * (y + 1) / 4;
       
 
       
        // closer to desired number of rectangles than before ?
       
        if (abs(bestRectangles - target) > abs(rectangles - target))
       
        {
       
          bestRectangles = rectangles;
       
          bestArea       = area;
       
        }
       
 
       
        // prefer larger areas, too (additional requirement of Hackerrank)
       
        if (abs(bestRectangles - target) == abs(rectangles - target) && bestArea < area)
       
          bestArea = area;
       
 
       
        y++;
       
      } while (rectangles < target);
       
 
       
      // just a speed-up ... abortion when the inner loop exited with a square area x*y
       
      // => it means that no further solutions possible, area already too large
       
      if (y == x + 1) // plus one because y was incremented before leaving the inner loop
       
        break;
       
    }
       
    std::cout << bestArea << std::endl;
       
  }
       
  return 0;
       
}

This solution contains 8 empty lines, 9 comments and 2 preprocessor commands.