Question

triangles abc and def are similar. find the length of segment ef.
a 5 cm
b 8.8 cm
c 12 cm
d 14 cm
e 18.75 cm

Explanation:

Step1: Identify Corresponding Sides

In similar triangles, corresponding sides are proportional. Let's assume side \( AB = 5 \, \text{cm} \), \( DE = 4 \, \text{cm} \), and \( BC = 11 \, \text{cm} \). We need to find \( EF \) (corresponding to \( BC \)).

Step2: Set Up Proportion

The ratio of corresponding sides should be equal. So, \( \frac{AB}{DE}=\frac{BC}{EF} \). Substituting the known values: \( \frac{5}{4}=\frac{11}{EF} \). Wait, no, wait—wait, maybe I mixed up. Wait, looking at the triangles, maybe \( AB = 5 \), \( DE = 4 \), and \( BC = 11 \), or maybe \( AB = 5 \), \( DE = 4 \), and \( AC = 15 \)? Wait, no, the first triangle has sides 5, 11, 15? Wait, no, the first triangle: \( AB = 5 \, \text{cm} \), \( BC = 11 \, \text{cm} \), \( AC = 15 \, \text{cm} \)? Wait, no, the second triangle has a side \( DE = 4 \, \text{cm} \). Wait, maybe the corresponding sides are \( AB \) and \( DE \), \( BC \) and \( EF \), \( AC \) and \( DF \). Wait, let's check again.

Wait, the first triangle: sides \( AB = 5 \, \text{cm} \), \( BC = 11 \, \text{cm} \), \( AC = 15 \, \text{cm} \)? No, the labels: \( B \), \( C \), \( A \)? Wait, the first triangle is \( ABC \), with \( AB = 5 \), \( BC = 11 \), \( AC = 15 \)? Wait, no, the second triangle is \( DEF \), with \( DE = 4 \). Wait, maybe the ratio is \( AB/DE = BC/EF \). So \( AB = 5 \), \( DE = 4 \), \( BC = 11 \), so \( 5/4 = 11/EF \)? No, that would give \( EF = (11 \times 4)/5 = 44/5 = 8.8 \). Wait, that makes sense. Let's verify:

\( \frac{AB}{DE}=\frac{BC}{EF} \)

\( \frac{5}{4}=\frac{11}{EF} \)

Cross - multiply: \( 5 \times EF = 4 \times 11 \)

\( 5EF = 44 \)

\( EF=\frac{44}{5}=8.8 \, \text{cm} \)

Answer:

B. 8.8 cm