Question

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

Answer 1

Answer:

DF = 13.5

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:

$\frac{EF}{BC}=\frac{DF}{AC}$

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

$\frac{6}{4}=\frac{DF}{9}$

Then, we can solve for DF:

$\begin{gathered} \frac{6}{4}\times9=\frac{DF}{9}\times9 \\ \frac{6\times9}{4}=DF \\ \frac{54}{4}=DF \\ 13.5=DF \end{gathered}$

Therefore, the length of side DF is 13.5