Question

the square on the right is a scaled copy of the square on the left. identify the scale factor. express your answer as a fraction in simplest form. there are two squares: the top square has side length 27, the bottom square has side length 6

Explanation:

Step1: Recall scale factor formula

The scale factor from the original figure (left square) to the scaled copy (right square) is the ratio of the side length of the copy to the side length of the original. Let the original side length be \( s_{original} = 27 \) and the copy side length be \( s_{copy}=6 \). The scale factor \( k=\frac{s_{copy}}{s_{original}} \).

Step2: Substitute values and simplify

Substitute \( s_{copy} = 6 \) and \( s_{original}=27 \) into the formula: \( k=\frac{6}{27} \). Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 3. So, \( \frac{6\div3}{27\div3}=\frac{2}{9} \).

Answer:

\(\frac{2}{9}\)