We know that the corresponding sides of the two triangles must be proportional. Therefore, we know that the proportion 9:6 will hold for all of the sides.
For the longest side of the second triangle, we use the following equation:
9/6 = 18/x
Now we cross multiply to find for x.
9x = 108 or x = 12
So the length of the longest side of the second triangle is 12 units.
The ratio of sides of the first triangle is 9:15:18.
The ratio of sides of the similar triangle is 6:X:Y.
Now, we'll determine the proportion:
6/9 = a
We'll cross multiply and we'll get:
9a = 6
We'll divide by 3:
3a = 2
a = 2/3
We'll multiply each known length of the side by the proportion a:
9*(2/3) = 6
15*(2/3) = 10
18*(2/3) = 12
The length of the longest side of the triangle is of 12 units.