If Triangle A B C and Triangle D E F are similar, it means that their corresponding sides are proportional. We can use this information to find the length of DF.
Let x be the length of DF. Then, we can set up the following proportion:
AB/DE = AC/DF
Substituting the given values, we get:
6/10 = 15/x
Cross-multiplying, we get:
6x = 150
Dividing both sides by 6, we get:
x = 25
Therefore, the length of DF is 25.