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 $k$ from the original figure to the scaled - copy is given by $k=\frac{\text{length in scaled copy}}{\text{length in original}}$.

Step2: Select corresponding sides

Let's take the vertical sides of the two right - triangles. The vertical side of the original triangle is $6$, and the vertical side of the scaled copy is $\frac{15}{2}$.

Step3: Calculate the scale factor

$k = \frac{\frac{15}{2}}{6}=\frac{15}{2}\times\frac{1}{6}=\frac{15}{12}=\frac{5}{4}$

Answer:

$\frac{5}{4}$