Question

in the figure below, abc and def are similar triangles with the given side lengths in meters. what is the perimeter of def? a. 3 b. 8 c. 11 d. 12

Explanation:

Step1: Find the scale - factor

The ratio of corresponding sides of similar triangles is the same. Let's find the scale - factor using the sides $AC = 10$ and $DF = 5$. The scale - factor $k=\frac{DF}{AC}=\frac{5}{10}=\frac{1}{2}$.

Step2: Find the length of $DE$

Since $\triangle ABC\sim\triangle DEF$, and $AB = 6$, then $DE=\frac{1}{2}\times AB=\frac{1}{2}\times6 = 3$.

Step3: Find the perimeter of $\triangle DEF$

The sides of $\triangle DEF$ are $DE = 3$, $EF = 3$, and $DF = 5$. The perimeter $P$ of $\triangle DEF$ is $P=DE + EF+DF=3 + 3+5=11$.

Answer:

c. 11