An isosceles triangle has legs that are 15 cm and a perimeter of 48 cm. What is the perimeter of a similar isosceles triangle with a base of 12 cm?

The ratio of a side to the perimeter is 15:48 = 5:16

You have the same ratio for the bigger triangle since they are similar.
12:P

where this is equal to 5:16

Hence, you have:

\frac{12}{P} = \frac{5}{16}

Find P