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: Identify corresponding sides

Let the side - lengths of the smaller triangle be \(a = 6\) and \(b = 8\), and the side - lengths of the larger triangle be \(A=18\) and \(B = 24\). We can use the ratio of corresponding sides to find the scale factor. Let's use the ratio of the horizontal sides.

Step2: Calculate the scale factor

The scale factor \(k\) is given by the ratio of the length of a side of the larger triangle to the length of the corresponding side of the smaller triangle. Using the horizontal sides, \(k=\frac{18}{6}\).
\[k = 3\]

Answer:

3