Question

question 40 of 40 if △abc~△def and the scale factor from △abc to △def is 1/5, what are the lengths of (overline{de}), (overline{ef}), and (overline{df}), respectively? a. 10, 10, 25 b. 2, 2, 5 c. 5, 5, 15 d. 5, 5, 5

Explanation:

Step1: Recall scale - factor formula

If the scale factor from $\triangle ABC$ to $\triangle DEF$ is $k=\frac{1}{5}$, and the side - lengths of $\triangle ABC$ are $a = 10$, $b = 10$, $c = 25$. The side - lengths of $\triangle DEF$ (say $d$, $e$, $f$) are given by $d=k\times a$, $e = k\times b$, $f=k\times c$.

Step2: Calculate side - lengths of $\triangle DEF$

For side $DE$: $d=\frac{1}{5}\times10 = 2$.
For side $EF$: $e=\frac{1}{5}\times10 = 2$.
For side $DF$: $f=\frac{1}{5}\times25 = 5$.

Answer:

B. 2, 2, 5