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: Determine corresponding sides

The left triangle has a side length of 65, and the right (scaled) triangle has a corresponding side length of 26. The scale factor is the ratio of the length of the scaled triangle's side to the original triangle's side. So we calculate $\frac{26}{65}$.

Step2: Simplify the fraction

To simplify $\frac{26}{65}$, we find the greatest common divisor (GCD) of 26 and 65. The factors of 26 are 1, 2, 13, 26. The factors of 65 are 1, 5, 13, 65. The GCD is 13. Divide both the numerator and the denominator by 13: $\frac{26\div13}{65\div13}=\frac{2}{5}$.

Answer:

$\frac{2}{5}$