triangle abc is similar to def. the length of ef is 7 inches, while the length of bc is 5 inches. if the length of ab is 16 inches, what is the length of de?

Ok . since they are similar you can use similarity factor

When you are talking about similarity between triangles... you are talking about using a proportion. in this case..
1) ABC ~ DEF,
2) 5/7 = 16/x, now we are using the variable X because we don't know the value of DE..
3) Now, you cross multiply... you should get something like ---> 5x=112
4)divide 5 both sides
5) you get X=22.4
so the length of DE is 22.4
I HOPE I HELPED.