Question

a four - sided figure is resized to create a scaled copy. the lengths of its four sides change as in the table below. find the scale factor as a fraction in reduced terms.

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(=\frac{\text{Length of scaled copy}}{\text{Length of original figure}}\)

Step2: Calculate scale factor using first pair of values

Using \(15\) (original) and \(5\) (scaled copy), scale factor \(=\frac{5}{15}=\frac{1}{3}\)

Step3: Verify with other pairs

For \(21\) (original) and \(7\) (scaled copy), \(\frac{7}{21}=\frac{1}{3}\)
For \(36\) (original) and \(12\) (scaled copy), \(\frac{12}{36}=\frac{1}{3}\)

Answer:

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