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 an original figure to a scaled - copy is given by \(k=\frac{\text{corresponding side length in scaled copy}}{\text{corresponding side length in original figure}}\).

Step2: Identify corresponding side lengths

Let the original rectangle have side lengths \(15\) and \(45\), and the scaled - copy rectangle have side lengths \(5\) and \(15\). We can use either pair of corresponding sides. Using the shorter sides, the side length in the original rectangle is \(15\) and the side length in the scaled copy is \(5\).

Step3: Calculate the scale factor

\(k = \frac{5}{15}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)