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 scale - factor formula

The scale factor $k$ from the original figure to the scaled - copy is given by the ratio of the corresponding side lengths of the scaled - copy to the original figure. Let the side length of the original triangle be $a = 75$ and the side length of the scaled - copy be $b = 30$.

Step2: Calculate the scale factor

$k=\frac{b}{a}=\frac{30}{75}$

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 30 and 75. The GCD of 30 and 75 is 15. Divide both the numerator and the denominator by 15: $\frac{30\div15}{75\div15}=\frac{2}{5}$

Answer:

$\frac{2}{5}$