Question

question 13 of 33
if △abc ~ △def and the scale factor from △abc to △def is 1/7, what are the lengths of (overline{de}), (overline{ef}), and (overline{df}), respectively?
a. 35, 21, 42
b. 21, 7, 28
c. 196, 98, 245
d. 4, 5, 2

Explanation:

Step1: Recall similar - triangle property

If $\triangle ABC\sim\triangle DEF$ and the scale factor from $\triangle ABC$ to $\triangle DEF$ is $\frac{1}{7}$, then if the side - lengths of $\triangle ABC$ are $AB = 28$, $BC = 35$, $AC = 14$, the side - lengths of $\triangle DEF$ are obtained by multiplying the side - lengths of $\triangle ABC$ by $\frac{1}{7}$.

Step2: Calculate $DE$

$DE=\frac{1}{7}\times AB$. Since $AB = 28$, then $DE=\frac{1}{7}\times28 = 4$.

Step3: Calculate $EF$

$EF=\frac{1}{7}\times BC$. Since $BC = 35$, then $EF=\frac{1}{7}\times35 = 5$.

Step4: Calculate $DF$

$DF=\frac{1}{7}\times AC$. Since $AC = 14$, then $DF=\frac{1}{7}\times14 = 2$.

Answer:

D. 4, 5, 2