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x = 10; y = 12

Step-by-step explanation:

find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2

from large triangle to small triangle you will get:

1. 15 / x

2. 18 / y

to implement the ratio, set the side length ratio equal to the scale factor:

1. =

2. =

cross multiply:

1. 30 = 3x

2. 36 = 3y

divide:

1. x = 10

2. y = 12