Question

May I please get help with this. I have tried many times and different ways to get the correct answer for this but I still can’t seem to figure it out and get the right answer

Answer 1

20

Step-by-step explanation:

Recall that two triangles are said to be similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.

So given that triangles ABC and DEF are similar, we have to determine the missing side length by setting up proportions as seen below;

`\begin{gathered} (AB)/(DE)=(BC)/(EF) \\ (4)/(DE)=(8)/(40) \end{gathered}`

Let's cross multiply;

`\begin{gathered} 8\cdot DE=4\cdot40 \\ 8DE=160 \end{gathered}`

Let's divide both sides by 8;

`\begin{gathered} (8DE)/(8)=(160)/(8) \\ DE=20 \end{gathered}`

So the missing side length is 20