Question

1. if δabc is similar to δdef, what must be the length of \\(\overline{ac}\\)? images of triangles abc and def with side lengths: ab = 6 cm, de = 4 cm, df = 10 cm, ac = ?. multiple choice options: 8, 18, 12, 15

Explanation:

Step1: Identify corresponding sides

In similar triangles \( \triangle ABC \) and \( \triangle DEF \), the corresponding sides are proportional. \( AB \) corresponds to \( DE \), and \( AC \) corresponds to \( DF \). Given \( AB = 6 \, \text{cm} \), \( DE = 4 \, \text{cm} \), and \( DF = 10 \, \text{cm} \).

Step2: Set up proportion

Let \( AC = x \). The proportion is \( \frac{AB}{DE} = \frac{AC}{DF} \), so \( \frac{6}{4} = \frac{x}{10} \).

Step3: Solve for \( x \)

Cross - multiply: \( 4x = 6\times10 \). Then \( 4x = 60 \), and \( x=\frac{60}{4}=15 \).

Answer:

15