Question

side length in original rectangle, corresponding side length in scaled copy, 10, 2, 15, 3, the scale factor is

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from the original figure to the scaled - copy is given by $k=\frac{\text{side length in scaled copy}}{\text{side length in original figure}}$.

Step2: Use the first pair of side - lengths

Using the first row of the table where the side length in the original rectangle is $10$ and the corresponding side length in the scaled copy is $2$, we calculate $k_1=\frac{2}{10}=\frac{1}{5}$.

Step3: Check with the second pair of side - lengths

Using the second row of the table where the side length in the original rectangle is $15$ and the corresponding side length in the scaled copy is $3$, we calculate $k_2=\frac{3}{15}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$