The value of x of the similar triangles is: x = 22.5 cm
How to find the length of similar triangles?
Two triangles are said to be similar if the ratio of the lengths of their corresponding sides are congruent.
In the figure attached the graph of the problem can be seen.
Given the triangles are similar then the next proportion must be satisfied:
13.5/9 = 18/12
= x/15 = 1.5
Isolating x, we get:
x/15 = 1.5
x = 1.5*15
x = 22.5 cm