A printed page is to have 1.5 inches margin on all sides. The page should contain 144 square inches of type. What dimension of the page will minimize the area while still meeting these other requirements?

Answer 1

If there is no limit to the dimensions of the page, a square will have minimal area. If the printed area is

12x12, the sheet is 15x15 with area 225
6x24, the sheet is 9x27 with area 243
1x144, the sheet is 4x147 with area 588.

I think you have left out some pertinent constraints.
.1x1440, the sheet is 3.1x1443 with area 4473