Question

i \can\ similarity δabc ~ δdef. what is the perimeter of δdef. (triangle abc with sides ab=12, bc=15, ac=19; triangle def with sides fd=30.4, de=19.2) a 88.2 b 73.6 c 80.3 d 38.1

Explanation:

Step1: Calculate the perimeter of $\triangle ABC$

The perimeter of $\triangle ABC$ is $P_{ABC}=12 + 15+19=46$.

Step2: Find the scale factor

Since $\triangle ABC\sim\triangle DEF$, the scale factor $k$ is determined by the ratio of corresponding sides. Let's use the sides $AC = 19$ and $EF=30.4$. The scale factor $k=\frac{EF}{AC}=\frac{30.4}{19} = 1.6$.

Step3: Calculate the perimeter of $\triangle DEF$

For similar triangles, the ratio of perimeters is equal to the scale factor. Let $P_{DEF}$ be the perimeter of $\triangle DEF$. We know that $\frac{P_{DEF}}{P_{ABC}}=k$. Substituting $P_{ABC} = 46$ and $k = 1.6$, we get $P_{DEF}=46\times1.6$.
$P_{DEF}=73.6$

Answer:

B. 73.6