Final answer:
To build a set of square tiles where adding a tile decreases the perimeter, use an L-shaped formation. Adding a tile to the 'crook' of the L will fill a gap and reduce the total perimeter. Remember that perimeter is measured in linear units, while area is measured in square units.
Step-by-step explanation:
The question posed is a mathematical problem that involves understanding the concept of perimeter in geometry. To create a set of square tiles where adding a tile decreases the perimeter, you can use an L-shaped formation of tiles. If you add a tile to the 'crook' of the L, the perimeter actually decreases because you are filling in a gap.
For example, imagine you have an L-shaped figure made of 3 tiles tall and 3 tiles wide, without the corner tile (so there are 5 tiles in total). The perimeter of this shape would be 12 units because you have 3 sides of the outer layer that are each 3 units long and the two inner sides are each 1.5 units long, as you might be imagining half tiles. By adding one tile to complete the square corner, the perimeter decreases to 10 units.
A helpful trick to remember is how the perimeter and area of shapes work. For a square with side length a, the perimeter is 4a and the area is a². The units also matter: perimeter is in linear units (like meters) and area is in square units (like square meters). This helps to avoid confusion between measurements of perimeter and area, as they are fundamentally different.