Question

1. triangle abc and triangle def are scaled copies. side ab measures 12 cm and is the longest side of abc. side de measures 8 cm and is the longest side of def.

a. triangle abc is a scaled copy of triangle def with what scale factor?

Explanation:

Step1: Recall scale - factor formula

The scale factor from triangle $DEF$ to triangle $ABC$ is given by the ratio of the corresponding side lengths of $ABC$ to $DEF$.
Let the scale factor be $k$. Then $k=\frac{\text{length of corresponding side in }ABC}{\text{length of corresponding side in }DEF}$.

Step2: Identify corresponding sides

The longest side of $ABC$ is $AB = 12$ cm and the longest side of $DEF$ is $DE = 8$ cm. These are corresponding sides.

Step3: Calculate the scale factor

$k=\frac{AB}{DE}=\frac{12}{8}=\frac{3}{2}=1.5$

Answer:

$1.5$