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.
54
54
12
12

Explanation:

Step1: Recall scale factor formula

Scale factor is the ratio of corresponding side lengths of the scaled copy to the original figure. Here, the right triangle on the right is the scaled copy (or maybe the left is original, but we take corresponding sides: let's take the side of the scaled copy (right) over original (left) or vice versa? Wait, the right is a scaled copy of the left. So scaled copy (right) side length divided by original (left) side length.

Corresponding sides: left triangle has side 54, right has 12 (or left 54, right 12 for another side). Let's take the vertical sides: left is 54, right is 12. Or horizontal: left 54, right 12.

Step2: Calculate the ratio

So scale factor = (length of scaled copy side) / (length of original side) = \( \frac{12}{54} \). Simplify this fraction. Divide numerator and denominator by 6: \( \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \)? Wait, no: wait, wait, maybe I got original and scaled copy reversed. Wait, the problem says "the right triangle on the right is a scaled copy of the right triangle on the left". So left is original, right is scaled copy. So scaled copy (right) is smaller, so scale factor is scaled / original = 12/54? Wait, but 12 and 54: GCD is 6. 12÷6=2, 54÷6=9. Wait, but maybe I had it reversed. Wait, no: if the right is a scaled copy of the left, then the left is the original, right is the image. So scale factor is image side / original side. So 12/54 = 2/9? Wait, but let's check: original side 54, scaled side 12. So 12 = 54 * k, so k = 12/54 = 2/9. Yes.

Wait, but let's confirm. Scale factor: if you scale the original (left) by k to get the scaled copy (right), then scaled side = original side * k. So k = scaled / original = 12/54 = 2/9.

Answer:

\( \frac{2}{9} \)