Question

1. triangle abc is similar to triangle dbe. $overline{ac} : overline{de}$ is 3:2 and the length of $overline{ab}$ is 42. what is the length of $overline{db}$? image of triangle with points a, b, c, d, e options: 16.8, 14, 28, 21

Explanation:

Step1: Recall similarity ratio

For similar triangles \( \triangle ABC \) and \( \triangle DBE \), the ratio of corresponding sides is equal. Given \( \frac{AC}{DE}=\frac{3}{2} \), so the ratio of similarity \( \frac{AB}{DB}=\frac{AC}{DE}=\frac{3}{2} \).

Step2: Set up proportion

Let \( DB = x \). We know \( AB = 42 \), so the proportion is \( \frac{42}{x}=\frac{3}{2} \).

Step3: Solve for \( x \)

Cross - multiply: \( 3x = 42\times2 \).
Simplify: \( 3x = 84 \).
Divide both sides by 3: \( x=\frac{84}{3}=28 \).

Answer:

28