Neela is making rectangular place mats that are 12 inches wide and 15 inches long. what is the least amount of ribbon that she will need to create a ribbon border around 1 place mat?

Believe it or not, :), the width of the ribbon needs to be known to get the right answer.  If the ribbon had an infinitely small width the ribbon needed would just be the perimeter.

P=2(L+W)

P=2(12+15)

P=54 in

However an infinitely small width is not something that has any practical application.  For example, if the width of the ribbon were 1/2 in.

P=2((L+1)+W)

P=2(16+12)

P=56 in  So the perimeter increased by 2 in when the ribbon was only 1/2 in wide.

The "infinitely small" width and the perimeter of 54 in is only a decent approximation if the ribbon were a very thin string.