Question

the triangle on the right is a scaled copy of the triangle on the left. identify the scale factor. express your answer as a fraction in simplest form.

Explanation:

Step1: Recall scale factor formula

Scale factor is the ratio of corresponding side lengths of the scaled copy to the original. Let the original triangle (left) have side length \( 16 \), and the scaled copy (right) have corresponding side length \( 26 \). So scale factor \( = \frac{\text{Scaled length}}{\text{Original length}} \).

Step2: Calculate the scale factor

Substitute the values: \( \frac{26}{16} \). Simplify this fraction by dividing numerator and denominator by their greatest common divisor, which is \( 2 \). So \( \frac{26 \div 2}{16 \div 2} = \frac{13}{8} \). Wait, no—wait, wait. Wait, actually, the left is original, right is scaled. Wait, no: wait, the left triangle has sides 16, 16. The right has 26, 26. So scale factor is (right side)/(left side) = 26/16? Wait, no, wait—wait, maybe I mixed up. Wait, the problem says "the triangle on the right is a scaled copy of the triangle on the left". So scaled copy (right) is a copy of original (left), so scale factor is (length of scaled)/(length of original). So original side is 16, scaled side is 26. So \( \frac{26}{16} \) simplifies to \( \frac{13}{8} \)? Wait, no, wait—wait, 26 and 16: GCD of 26 and 16 is 2. 26 ÷ 2 = 13, 16 ÷ 2 = 8. So \( \frac{26}{16} = \frac{13}{8} \)? Wait, no, wait—wait, maybe I got original and scaled reversed? Wait, no: if the right is a scaled copy of the left, then the left is original, right is scaled. So scale factor is (right side)/(left side) = 26/16 = 13/8. Wait, but let me check again. Original triangle (left) has side 16, scaled (right) has 26. So scale factor is 26/16 = 13/8. Wait, but maybe I made a mistake. Wait, 26 divided by 16: 26 ÷ 2 = 13, 16 ÷ 2 = 8. So yes, 13/8. Wait, but let me confirm the formula. Scale factor for a scaled copy: if the copy is larger, scale factor is greater than 1. Here, right triangle is larger, so scale factor is 26/16 = 13/8.

Answer:

\(\frac{13}{8}\)