Question

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

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from a pre - image to an image is given by $k=\frac{\text{length in image}}{\text{length in pre - image}}$.

Step2: Determine scale factor for part a

If $\triangle ABC$ is a scaled copy of $\triangle DEF$, then the scale factor $k_1=\frac{AB}{DE}$. Given $AB = 12$ cm and $DE=8$ cm, so $k_1=\frac{12}{8}=\frac{3}{2}$.

Step3: Determine scale factor for part b

If $\triangle DEF$ is a scaled copy of $\triangle ABC$, then the scale factor $k_2=\frac{DE}{AB}$. Given $AB = 12$ cm and $DE = 8$ cm, so $k_2=\frac{8}{12}=\frac{2}{3}$.

Answer:

a. The scale factor is $\frac{3}{2}$.
b. The scale factor is $\frac{2}{3}$.