Question

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

Explanation:

Step1: Recall Scale Factor Formula

The scale factor from the original (left) to the scaled (right) figure is the ratio of a side length of the scaled figure to the corresponding side length of the original figure. Let the original side length be \( a = 10 \) and the scaled side length be \( b = 28 \). The scale factor \( k=\frac{b}{a} \).

Step2: Calculate the Ratio

Substitute the values: \( k = \frac{28}{10} \). Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 2. So, \( \frac{28\div2}{10\div2}=\frac{14}{5} \).

Answer:

\(\frac{14}{5}\)