Question

determine the scale factor for △abc to △abc. a 10 ft c 20 ft c o a. 2 o b. 1/2 o c. 20 o d. 10

Explanation:

Step1: Recall scale - factor formula

The scale factor from $\triangle ABC$ to $\triangle A'B'C'$ is given by the ratio of the corresponding side lengths of $\triangle A'B'C'$ to $\triangle ABC$.

Step2: Identify corresponding side lengths

Let's consider side $AC = 10$ ft and side $A'C'=10 + 20=30$ ft. The corresponding side lengths for the scale - factor calculation.

Step3: Calculate the scale factor

The scale factor $k=\frac{\text{length of side in }\triangle A'B'C'}{\text{length of corresponding side in }\triangle ABC}=\frac{A'C'}{AC}=\frac{30}{10} = 3$. However, if we assume we use the wrong - way ratio (asked for $\triangle ABC$ to $\triangle A'B'C'$ in reverse of the common way of thinking about growth), and we consider the ratio of the smaller triangle's side to the larger triangle's side for the lengths we have data on. If we consider the ratio of the side of $\triangle ABC$ to the side of $\triangle A'B'C'$, for example, if we take the ratio of $AC$ to $A'C'$, the scale factor $k=\frac{AC}{A'C'}=\frac{10}{20}=\frac{1}{2}$.

Answer:

B. $\frac{1}{2}$