Question

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

Explanation:

Step1: Determine the scale factor direction

We need to find the scale factor from the left square (side length 25) to the right square (side length 32) or vice versa? Wait, the problem says "the square on the right is a scaled copy of the square on the left". So left is original, right is copy. Wait, no, wait: the left square (the lower one) has side 25, the right square (upper) has side 32? Wait, no, looking at the image: the upper square is labeled 32 (top and right), the lower square is labeled 25 (top and right). The problem says "the square on the right is a scaled copy of the square on the left". Wait, maybe I got left and right reversed. Wait, the text says "the square on the right is a scaled copy of the square on the left". So the left square (lower one, side 25) is the original, the right square (upper one, side 32) is the copy? Wait, no, maybe the other way: maybe the upper square is the original, and the lower is the copy? Wait, the problem says "the square on the right is a scaled copy of the square on the left". So left is original, right is copy. Wait, the left square (lower) has side 25, right square (upper) has side 32. Wait, no, maybe I misread: the upper square is on the right? Wait, the image: upper square is 32, lower square is 25. The text says "the square on the right is a scaled copy of the square on the left". So left square (lower, side 25) is original, right square (upper, side 32) is copy? Wait, no, that would mean scale factor is 32/25, but maybe the other way: maybe the upper square is the original, and the lower is the copy. Wait, the problem says "the square on the right is a scaled copy of the square on the left". So left is original, right is copy. So original side length: let's check the labels. The lower square (left?) has side 25, upper square (right) has side 32. Wait, maybe the left square is the upper one (32) and the right square is the lower one (25)? No, the text says "the square on the right is a scaled copy of the square on the left". So left square (upper, 32) is original, right square (lower, 25) is copy? Wait, that would make scale factor 25/32. Wait, the problem says "identify the scale factor". Let's re-read: "The square on the right is a scaled copy of the square on the left. Identify the scale factor." So left square (original) and right square (copy). So we need to find the ratio of the side length of the copy to the original. Wait, the left square: which one is left? The upper square is on the right? Wait, the image: upper square is 32, lower square is 25. So maybe the left square is the lower one (25) and the right square is the upper one (32). So original side length: 25 (left), copy side length: 32 (right). Then scale factor is 32/25? Wait, no, that would be scaling up. But maybe the other way: maybe the left square is the upper one (32) and the right square is the lower one (25). So original side length: 32 (left), copy side length: 25 (right). Then scale factor is 25/32. Wait, the problem says "express your answer as a fraction in simplest form". Let's check the sides: the upper square has side 32, lower square has side 25. The problem says "the square on the right is a scaled copy of the square on the left". So left square (original) and right square (copy). So we need to find the ratio of the copy's side to the original's side. So if left is lower (25) and right is upper (32), then scale factor is 32/25. If left is upper (32) and right is lower (25), then scale factor is 25/32. Wait, maybe the problem is that the square on the right (upper) is a scaled copy of the square on the left (lower). So original (left) has side 25, copy (right) has side 32. Then scale factor is 32/25. But 32 and 25 have no common factors (25 is 5², 32 is 2⁵), so that's simplest form. Wait, but maybe I got it reversed. Wait, the problem says "the square on the right is a scaled copy of the square on the left". So left is original, right is copy. So we take the side length of the copy (right) divided by the side length of the original (left). So if left square (lower) has side 25, right square (upper) has side 32, then scale factor is 32/25. Wait, but 32/25 is greater than 1, meaning an enlargement. Alternatively, if the left square is the upper one (32) and the right square is the lower one (25), then scale factor is 25/32, which is a reduction. Which makes sense? The lower square is smaller, so maybe it's a scaled copy (reduction) of the upper square. Wait, the problem says "the square on the right is a scaled copy of the square on the left". So "right" square is the copy, "left" square is the original. So if the right square is the lower one (25) and the left square is the upper one (32), then scale factor is 25/32. Let's confirm: scale factor is (length of copy) / (length of original). So if original is left (upper, 32), copy is right (lower, 25), then scale factor is 25/32. That makes sense because 25 is less than 32, so it's a reduction. Let's check the labels: the upper square (left?) has 32, lower square (right?) has 25. The problem says "the square on the right is a scaled copy of the square on the left". So left square (upper, 32) is original, right square (lower, 25) is copy. Therefore, scale factor is 25/32.

Step1: Identify original and copy sides

Original square (left) side: 32
Copy square (right) side: 25

Step2: Calculate scale factor

Scale factor = (Copy side) / (Original side) = $\frac{25}{32}$
(25 and 32 have no common factors, so it's in simplest form)

Answer:

$\frac{25}{32}$