An original piece of art work is 3 feet by 2.5 feet. a reprint of the artwork is 6 inches by 5 inches. are the pieces similar? if so, what is the ratio of their corresponding side lengths?

For this case we observe that the dimensions of the original piece are:
 3 feet
 2.5 feet
 Let's multiply these dimensions by a scale factor k:
 3 * k
 2.5 * k
 We match the new dimensions with their respective values:
 3 * k = 6
 2.5 * k = 5
 Clearing k we have:
 k = 6/3 = 2
 k = 5 / 2.5 = 2
 Since the value of k is the same, then the pieces are similar.
 
 The pieces are similar.
 The ratio of their corresponding side lengths is: 
 k = 2