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.

Answer:

The pieces are similar.

The ratio of their corresponding side lengths is:

k = 2