Chapter E, Problem 7.4EX

To determine

To find: The the perimeter of $\Delta DEF$ .

Answer to Problem 7.4EX

the perimeter of $\Delta DEF=54$ .

Explanation of Solution

Given information: If $\Delta ABC\sim \Delta DEF$ and $AB=8,BC=12,AC=16,\text{ and }DE=12$ .

If $\Delta ABC\sim \Delta DEF$ and $AB=8,BC=12,AC=16,\text{ and }DE=12$ .

If the sides of two triangles are in proportion, then the triangles are similar.

So, in $\Delta ABC$ and $\Delta DEF$

  $\begin{array}{l}\frac{AB}{BC}=\frac{DE}{EF}\\ \text{Given }AB=8,BC=12,DE=12\end{array}$

Then

  $\begin{array}{l}\frac{8}{12}=\frac{12}{EF}\\ EF=18\end{array}$

And

  $\begin{array}{l}\frac{AC}{BC}=\frac{DF}{EF}\\ \text{Given }AC=16,BC=12,EF=18\\ \frac{16}{12}=\frac{DF}{18}\\ DF=24\end{array}$

So, the perimeter of $\Delta DEF=24+18+12$ .

the perimeter of $\Delta DEF=54$ .