Question

The sum of the perimeter of a square and a rectangle is 1,000 m. Find the dimensions of the square and the rectangle that will have a maximum area combined if the length of the rectangle is twice its width.

Answer 1

This is not your normal classroom maximum problem.
The maximum area is that of the square with a zero rectangular width.
Is it possible that the minimum area was requested?
A solution with a maximum square area of 62500 and a zero rectangular area is attached. The calculations are from the Mathematical 9 computer program.