Set up a proportion to solve for RT using the scale factor 3:1, and use it to find the length of RT.

To set up a proportion, we need two equivalent ratios or fractions. In this case, the scale factor given is 3:1, which represents the ratio of two corresponding lengths. Let's assume the length of the corresponding side on the smaller figure is x, and the length of the corresponding side on the larger figure is y.

Using the scale factor, we can write the proportion:

3/1 = y/x

Now, to solve for RT, we know that RT corresponds to y. So, we substitute y and the given information into the equation:

3/1 = RT/x

Cross-multiplying, we get:

3x = RT

To solve for RT, divide both sides of the equation by 3:

RT = 3x/3

RT = x

So, the length of RT is x, which corresponds to the corresponding side on the smaller figure.