Question

Determine the length of side DFTriangle ABC is similar to triangle DEF

Answer 1

DF = 13.5

Step-by-step explanation:

If the triangles are similar, the proportion between their corresponding sides is constant, so, if BC is corresponding to EF and AC is corresponding to DF, we get:

`(EF)/(BC)=(DF)/(AC)`

So, replacing EF by 6, BC by 4, and AC by 9, we get:

`(6)/(4)=(DF)/(9)`

Then, we can solve for DF:

`\begin{gathered} (6)/(4)*9=(DF)/(9)*9 \\ (6*9)/(4)=DF \\ (54)/(4)=DF \\ 13.5=DF \end{gathered}`

Therefore, the length of side DF is 13.5