Questions: For #s 7-8, use triangle XYZ as shown. 7. The shortest side of a triangle similar to triangle XYZ is 15 units long. Determine the other lengths of the triangle.

For #s 7-8, use triangle XYZ as shown. 7. The shortest side of a triangle similar to triangle XYZ is 15 units long. Determine the other lengths of the triangle.
Transcript text: For \#s 7-8, use $\triangle X Y Z$ as shown. 7. The shortest side of a triangle similar to $\triangle X Y Z$ is 15 units long. Determine the other lengths of the triangle.
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Solution

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Solution Steps

Step 1: Find the ratio of similitude

The shortest side of the given triangle XYZ is XZ, which has a length of 10. The shortest side of the similar triangle is given as 15. The ratio of similitude is the ratio of corresponding sides in similar triangles. Therefore, the ratio is 15/10 which simplifies to 3/2.

Step 2: Calculate the length of the second side

The second shortest side of triangle XYZ is YZ, with a length of 12. Multiply this length by the ratio of similitude to find the corresponding side length in the similar triangle: 12 * (3/2) = 18.

Step 3: Calculate the length of the third side

The longest side of triangle XYZ is XY, with a length of 13. Multiply this by the ratio of similitude: 13 * (3/2) = 39/2 = 19.5.

Final Answer

The other side lengths are 18 and 19.5.

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