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.
image of two triangles: left triangle with side length 8 (base) and 8 (leg); right triangle with side length 35 (base) and 35 (leg)
answer attempt 1 out of 2
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Explanation:

Step1: Recall scale factor formula

The scale factor from the original (left) to the copy (right) is the ratio of a side length of the copy to the corresponding side length of the original.

Step2: Identify corresponding sides

The left triangle has a side length of 8, and the corresponding side in the right triangle is 35.

Step3: Calculate scale factor

Scale factor = $\frac{\text{Length of copy side}}{\text{Length of original side}}$ = $\frac{35}{8}$? Wait, no—wait, wait. Wait, the right is the scaled copy of the left. Wait, no: "the triangle on the right is a scaled copy of the triangle on the left"—so original is left, copy is right. So scale factor is (copy side)/(original side). Wait, but let's check the sides. Left triangle: side 8, right triangle: side 35. Wait, no, maybe I mixed up. Wait, no—wait, the left triangle has sides 8 (both base and one leg), right triangle has sides 35 (both base and one leg). So to get from left to right, we multiply by scale factor. So scale factor = 35/8? Wait, no, wait—wait, maybe I got it reversed. Wait, no: scaled copy—so if the right is the copy, then scale factor is (copy length)/(original length). So original length (left) is 8, copy length (right) is 35. So scale factor is 35/8? Wait, but 35 and 8 have no common factors, so that's the simplest form. Wait, but let me confirm: scale factor is (length of image)/(length of pre - image). Pre - image is left (original), image is right (copy). So yes, 35/8. Wait, but maybe I made a mistake. Wait, no—let's see: if the left is original, right is copy, then scale factor is copy/original = 35/8. Yes.

Wait, wait, no—wait, maybe the left is the smaller one, right is larger. So scale factor is 35/8. Let me check: 8 * (35/8)=35, which matches the right triangle's side. So that's correct.

Answer:

$\frac{35}{8}$