Question

1. triangle abc is similar to triangle def. the length of side ab is 8, the length of side bc is 4, and the length of side de is 28. if the perimeter of triangle abc is 20, what is the perimeter of triangle def?

a. 40
b. 70
c. 112
d. 140

Explanation:

Step1: Find similarity ratio

The similarity ratio of $\triangle DEF$ to $\triangle ABC$ is $\frac{DE}{AB} = \frac{28}{8} = \frac{7}{2}$

Step2: Relate perimeters to ratio

For similar triangles, the ratio of perimeters equals the similarity ratio. Let $P_{DEF}$ be the perimeter of $\triangle DEF$, $P_{ABC}=20$.
$P_{DEF} = P_{ABC} \times \frac{7}{2}$

Step3: Calculate perimeter

$P_{DEF} = 20 \times \frac{7}{2} = 70$

Answer:

B. 70