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. 9 9 29 29

Explanation:

Step1: Recall scale factor formula

Scale factor is the ratio of corresponding sides of the scaled copy to the original. Let the left triangle be original, right be scaled. Corresponding sides: left has side 9, right has 29 (or left 9, right 29 for the other leg).

Step2: Calculate scale factor

Scale factor = $\frac{\text{Length of scaled side}}{\text{Length of original side}}$ = $\frac{29}{9}$? Wait, no—wait, wait, the left triangle has legs 9 and 9? Wait, no, the left triangle: one leg is 9, the other leg is 9? Wait, the right triangle: one leg is 29, the other leg is 29? Wait, no, the left triangle: horizontal side 9, vertical side 9. The right triangle: horizontal side 29, vertical side 29. Wait, no—wait, the right triangle is the scaled copy of the left. So scale factor is (scaled side)/(original side). So original side is 9, scaled is 29? Wait, no, maybe I got it 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. So corresponding sides: left has length 9 (say, vertical leg), right has vertical leg 29. So scale factor is 29/9? Wait, no, wait—wait, maybe the left is the smaller, right is larger. So scale factor is (length of right triangle's side)/(length of left triangle's side). So left side: 9, right side: 29. So scale factor is 29/9? Wait, but 9 and 29 are coprime? Wait, no, wait, maybe I misread. Wait, the left triangle: both legs are 9? So it's an isoceles right triangle. The right triangle: both legs are 29? So scale factor is 29/9. Wait, but let's check: scale factor is (scaled length)/(original length). So original length (left) is 9, scaled (right) is 29. So scale factor is 29/9. Wait, but 29 and 9 have no common factors, so that's simplest form.

Wait, no—wait, maybe the left is the scaled copy? No, 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. So corresponding sides: left leg 9, right leg 29. So scale factor is 29/9.

Answer:

$\frac{29}{9}$