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.

Explanation:

Step1: Identify corresponding sides

The left triangle has a side length of 9, and the right (scaled) triangle has a corresponding side length of 40.

Step2: Calculate scale factor

The scale factor is the ratio of the length of the scaled triangle's side to the original triangle's side. So, scale factor = $\frac{40}{9}$? Wait, no—wait, wait, the problem says "the right triangle on the right is a scaled copy of the right triangle on the left". Wait, no, looking at the labels: the left triangle has sides 9 and 9, the right (lower) triangle has sides 40 and 40. Wait, maybe I mixed up left and right. Wait, the text says: "The right triangle on the right is a scaled copy of the right triangle on the left". Wait, the left triangle (top) has sides 9, 9. The right triangle (bottom) has sides 40, 40. So the scale factor is (length of scaled side) / (length of original side). So original is 9, scaled is 40? Wait, no, maybe the bottom is the scaled copy of the top. So top is original, bottom is scaled. So corresponding sides: top has 9, bottom has 40. So scale factor is 40/9? Wait, but 9 and 40—wait, no, maybe I got left and right reversed. Wait, the problem says "the right triangle on the right is a scaled copy of the right triangle on the left". So left triangle (top) is original, right triangle (bottom) is scaled. So side lengths: original has 9, scaled has 40. So scale factor is 40/9? But 9 and 40 are coprime? Wait, no, wait, maybe the top 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 (top) is original, right (bottom) is scaled. So scale factor is (scaled length) / (original length) = 40/9? Wait, but 9 and 40—wait, maybe I misread the numbers. Wait, the top triangle: one side is 9, the other is 9. The bottom triangle: one side is 40, the other is 40. So yes, corresponding sides: 9 (original) and 40 (scaled). So scale factor is 40/9? Wait, but 9 and 40 have no common factors, so that's simplest form. Wait, but maybe I got it backwards. If the bottom is the original and the top is the scaled, then scale factor would be 9/40. But the problem says "the right triangle on the right is a scaled copy of the right triangle on the left". So left (top) is original, right (bottom) is scaled. So scale factor is 40/9. Wait, but let's check again. The problem: "Identify the scale factor. Express your answer as a fraction in simplest form." So original triangle (left, top) has side length 9. Scaled copy (right, bottom) has side length 40. So scale factor = scaled length / original length = 40/9. Wait, but 9 and 40 are coprime, so that's the simplest form.

Wait, maybe I made a mistake. Wait, the top triangle: sides 9, 9. Bottom triangle: sides 40, 40. So yes, corresponding sides. So scale factor is 40/9.

Answer:

$\frac{40}{9}$