Question

question 1 of 10
triangle abc is similar to triangle def. what is the length of
\\(\overline{de}\\)?

a. 18
b. 12
c. 10
d. 22

Explanation:

Step1: Identify Similar Triangles Ratio

Since \(\triangle ABC \sim \triangle DEF\), corresponding sides are proportional. So, \(\frac{AC}{DF}=\frac{AB}{DE}\). Given \(AC = 15\), \(DF = 10\), \(AB = 27\).

Step2: Set Up Proportion

\(\frac{15}{10}=\frac{27}{x}\) (where \(x = DE\)). Cross - multiply: \(15x=10\times27\).

Step3: Solve for \(x\)

\(15x = 270\), divide both sides by 15: \(x=\frac{270}{15}=18\).

Answer:

A. 18