# Triangle A has sides of lengths #15 #, #9 #, and #12 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

30,18

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Since the triangles are similar then the ratios of corresponding sides are equal.

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To find the possible lengths of the other two sides of triangle B, we use the concept of similarity between triangles. Since triangle B is similar to triangle A, their corresponding sides are proportional.

First, we need to find the scale factor between the two triangles. We can do this by comparing the corresponding sides of the two triangles.

The corresponding sides of triangle B to triangle A are in the ratio of 24:15 (the side we know in triangle B to the side we know in triangle A). Therefore, the scale factor is 24/15 or 8/5.

Now, to find the lengths of the other two sides of triangle B, we multiply each side of triangle A by the scale factor.

The possible lengths of the other two sides of triangle B are:

- Side corresponding to 9 in triangle A: 9 * 8/5 = 14.4
- Side corresponding to 12 in triangle A: 12 * 8/5 = 19.2

So, the possible lengths of the other two sides of triangle B are 14.4 and 19.2.

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