Question

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

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(=\frac{\text{length of side in new figure}}{\text{length of corresponding side in original figure}}\)

Step2: Identify the sides

Original side length \( = 27\), new side length \(=12\)

Step3: Calculate the scale factor

Scale factor \(=\frac{12}{27}\)

Step4: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (GCD). GCD of \(12\) and \(27\) is \(3\).
\(\frac{12\div3}{27\div3}=\frac{4}{9}\)

Answer:

\(\frac{4}{9}\)