Hi, there---

Problem:
A triangle has sides of 4, 9, and 12. In a similar triangle the shortest side is 12 and the longest is x. 
(a) write a proportion that models the situation
(b) solve the proptiortion for x

Solution:
(a) Similar triangles has the same shape, and the corresponding sides differ by a common scale factor.
Since 12 is the shortest side in the similar triangle, it is proportional to the side of 4 in the original triangle.
Since x is the longest side in the similar triangle, it is proportional to the side of 12 in the original triangle.
Therefore, one possible proportion is 

[similar shortest] / [original shortest] = [similar longest] / [original longest]

or

12/4 = x/12

(b) To solve the proportion, multiply both sides of the equation (proportion) by 12 to isolate x.

144/4 = x

Divide 144 by 4.

36 = x

The longest side of the similar triangle is 36.

Hope this helps. Feel free to email if you have questions about the solution.

Mrs. F
math.in.the.vortex@gmail.com