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 whole number or fraction in simplest form.

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) between two similar figures is the ratio of a corresponding side length of the scaled copy to the original figure's side length. So \( k=\frac{\text{Length of scaled copy}}{\text{Length of original}} \).

Step2: Identify corresponding sides

The original triangle (left) has a leg of length \( 5 \), and the scaled copy (right) has a corresponding leg of length \( \frac{25}{4} \).

Step3: Calculate scale factor

Substitute into the formula: \( k = \frac{\frac{25}{4}}{5} \). To divide by \( 5 \), we multiply by its reciprocal \( \frac{1}{5} \), so \( k=\frac{25}{4}\times\frac{1}{5}=\frac{25\times1}{4\times5}=\frac{5}{4} \).

Answer:

\(\frac{5}{4}\)