Question

the shortest side of a triangle similar to \\( \triangle xyz \\) is 20 units long. find the other side lengths of the triangle. the other side lengths are \\( \square \\) units and \\( \square \\) units.

Explanation:

Step1: Find the scale factor

The shortest side of \(\triangle XYZ\) is \(10\) units. The shortest side of the similar triangle is \(20\) units. The scale factor \(k=\frac{20}{10} = 2\).

Step2: Calculate the other side lengths

For the side of length \(12\) in \(\triangle XYZ\), the corresponding side length in the similar triangle is \(12\times k\). Substitute \(k = 2\), we get \(12\times2=24\).
For the side of length \(13\) in \(\triangle XYZ\), the corresponding side length in the similar triangle is \(13\times k\). Substitute \(k = 2\), we get \(13\times2 = 26\).

Answer:

The other side lengths are \(24\) units and \(26\) units.