How to Find the Scale Factor of a Triangle

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Similar triangles are objects that have the same shape and angle size, but their side lengths are different. The corresponding sides of the triangles, however, are in the same length ratio, also called the scale factor. Multiplying the smaller triangle's side lengths by the scale factor will give you the side lengths of the larger triangle. Similarly, dividing the larger triangle's side lengths by the scale factor will give you the side lengths of the smaller triangle.

    Set up ratios of the corresponding sides of the triangles. For example, the ratio of small to big triangle sides in two triangles is 5/10, 10/20 and 20/40.

    Divide both numbers in one of the ratios by their highest common factor. This will give you the scale factor of the bigger triangle to the smaller triangle. In the example, 5 is the highest common factor in the 5/10 ratio. Dividing 5 and 10 by 5 gives you a ratio of 1/2.

    Multiply the other sides in the larger triangle by the the ratio calculated in Step 2. In the example, when you multiply 20 by 1/2 and 40 by 1/2, you get 10 and 20, respectively. This confirms that the scale factor of the bigger triangle to the smaller triangle is 1/2.

    Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle. In the example, if you divided 40 by 20 you would get a scale factor of 2.

    Multiply the other sides in the smaller triangle by the the scale factor calculated in Step 4. In the example, when you multiply 5 by 2 and 10 by 2, you get 10 and 20, respectively. This confirms that the scale factor of the smaller triangle to the bigger triangle is 2.

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