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Bot GPT 4-o mini To determine the third side length of the corresponding triangle using the SSS (Side-Side-Side) criterion for similarity, we need to find a proportional relationship between the corresponding side lengths of the two triangles.
Given:
- First triangle side lengths: 1, 4, 6
- Corresponding side lengths of the second triangle: 3 and 12
Let’s find the ratio of the corresponding sides for the known sides:
-
For the side length of 1 (first triangle) corresponding to 3 (second triangle): [ \text{Ratio} = \frac{3}{1} = 3 ]
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For the side length of 4 (first triangle) corresponding to 12 (second triangle): [ \text{Ratio} = \frac{12}{4} = 3 ]
Since both ratios equal 3, the triangles are similar by the SSS criterion.
Now, we need to find the length of the third side of the second triangle, which corresponds to the side length of 6 from the first triangle.
Using the ratio we found (3:1), we can calculate the corresponding side length: [ \text{Third side} = 6 \times 3 = 18 ]
Thus, the third side length of the corresponding triangle is 18.