Perimeter of the rectangle = 16 m.
So, Length + Breadth of rectangle = 16 ÷ 2 = 8 m.
For the maximum area of the rectangle, the measure of the length and breadth of the rectangle should be equal or as close as possible.
In this case, the measure of the length of rectangle = 8 ÷ 2 = 4 m.
Measure of breadth of rectangle = 8 m - 4 m = 4 m.
So, the maximum area of the tile = 4 m x 4 m = 16 sq. m