Question

polygon d is a scaled copy of polygon c. polygon c has side - lengths 44, 12, 20. polygon d has side - lengths 27 1/2, 7 1/2, 12 1/2. what scale factor takes polygon c to polygon d?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from polygon $C$ to polygon $D$ is given by the ratio of corresponding side - lengths, $k=\frac{\text{side length in D}}{\text{side length in C}}$.

Step2: Choose a pair of corresponding sides

Let's use the side of length 44 in polygon $C$ and the corresponding side of length $27\frac{1}{2}$ in polygon $D$.
$k = \frac{27\frac{1}{2}}{44}=\frac{\frac{55}{2}}{44}$

Step3: Simplify the ratio

$\frac{\frac{55}{2}}{44}=\frac{55}{2}\times\frac{1}{44}=\frac{55}{88}=\frac{5}{8}$

Answer:

$\frac{5}{8}$