Question

problem 5
type the answers in the boxes below.
a. what is the length of segment de? 4.8 units
b. what is the length of segment ac? units

Explanation:

Step1: Find the ratio of similarity

Since triangles \(ABC\) and \(DEF\) are similar, the ratio of their corresponding sides is equal.
The ratio of \(BE\) to \(FE\) is \(\frac{4}{2.4}=\frac{5}{3}\)

Step2: Find the length of \(DE\)

We know that \(\frac{AB}{DE}=\frac{BC}{EF}\)
Given \(AB = 2\), \(EF=3\)
Let \(DE=x\), then \(\frac{2}{x}=\frac{4}{2.4}\)
Cross - multiply: \(4x=2\times2.4\)
\(x = 1.2\)

Step3: Find the length of \(AC\)

Let \(AC = y\)
We have \(\frac{y}{3}=\frac{4}{2.4}\)
Cross - multiply: \(2.4y=3\times4\)
\(y = 5\)

Answer:

a. \(1.2\) units
b. \(5\) units