Question

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. 4, 5, 2
b. 196, 98, 245
c. 21, 7, 28
d. 35, 21, 42

Explanation:

Step1: Recall scale - factor formula

If two similar triangles $\triangle ABC$ and $\triangle DEF$ have a scale - factor $k$, and the side lengths of $\triangle ABC$ are $AB$, $BC$, $AC$ and the side lengths of $\triangle DEF$ are $DE$, $EF$, $DF$, then $DE = k\times AB$, $EF = k\times BC$, $DF = k\times AC$. Here, $k=\frac{1}{7}$, $AB = 28$, $BC = 35$, $AC = 14$.

Step2: Calculate length of $\overline{DE}$

$DE=\frac{1}{7}\times AB=\frac{1}{7}\times28 = 4$.

Step3: Calculate length of $\overline{EF}$

$EF=\frac{1}{7}\times BC=\frac{1}{7}\times35 = 5$.

Step4: Calculate length of $\overline{DF}$

$DF=\frac{1}{7}\times AC=\frac{1}{7}\times14 = 2$.

Answer:

A. 4, 5, 2