Question

the rectangle on the right is a scaled copy of the rectangle on the left. identify the scale factor. express your answer as a whole number or fraction in simplest form.

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) from the original figure to the scaled - copy is given by the ratio of corresponding side lengths. Let the original rectangle have side lengths \(l_1\) and \(w_1\), and the scaled - copy have side lengths \(l_2\) and \(w_2\). The scale factor \(k=\frac{l_2}{l_1}=\frac{w_2}{w_1}\).

Step2: Identify corresponding side lengths

Let's assume the side of length \(10\) in the original rectangle corresponds to the side of length \(5\) in the scaled - copy.

Step3: Calculate the scale factor

Using the formula \(k = \frac{\text{side length of scaled - copy}}{\text{side length of original}}\), we have \(k=\frac{5}{10}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)