Question

the longest side of a triangle similar to \\( \triangle xyz \\) is 39 units long. find the other side lengths of the triangle. the other side lengths are \\( \square \\) units and \\( \square \\) units.

Explanation:

Step1: Calculate the scale factor

The longest side of \(\triangle XYZ\) is \(13\). The longest side of the similar triangle is \(39\). The scale factor \(k=\frac{39}{13} = 3\).

Step2: Find 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 \(k = 3\), we get \(12\times3=36\).
For the side of length \(10\) in \(\triangle XYZ\), the corresponding side length in the similar triangle is \(10\times k\). Substitute \(k = 3\), we get \(10\times3 = 30\).

Answer:

The other side lengths are \(30\) units and \(36\) units.