1) A celebration is scheduled at the end of a long distance bike race you have entered. A local baker has donated a three-tiered cake with square layers. The top measures 12 inches on each side. The baker then decides to decorate each layer with a ribbon of orange, blue, and white frosting around it.

a) How long a ribbon of frosting do you need for the top layer?

b) Each side of the middle layer will be 18 inches long. How long of a ribbon of frosting is needed for the middle layer?

c) In part b, notice that each side of the middle layer is 6 inches longer than the top layer is the perimeter of the middle layer also 6 inches longer than the top layer?

d) Each side of the bottom layer will be 24 inches. How long a ribbon of frosting is needed for the bottom layer?

e) The length of each side of the bottom layer is twice the length of a side of the top layer. Is the perimeter of the bottom layer twice the perimeter of the top layer?

3. In problem 2c, it appears that the side of a square is multiplied by a certain positive number, it's perimeter is affected in a predictable way. You can use algebra to prove this observation. Let the side of a square with length a be increased by a factor of n > 0. That is, multiply the length a of the side of the square by a positive number 'n'.

a) Write an expression that represents the perimeter of the new square.

b) Compare the result in part a with the expression for the perimeter of the original square.

c) Complete the following statement: If the side of a square is increased by a factor of a, then its perimeter is .

4. Recall that the length of the side of the middle square layer (12 inches) was 6 inches longer than the side of the top layer (18 inches). Although the perimeter of the middle layer (72 inches) is not 6 inches more than the perimeter of the top layer (48 inches), there is a relationship between the perimeters of these two squares. Determine this relationship.