Question

what is the missing side length y in triangle xyz?
12
13
25
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question 6
triangle rst has side lengths 5 cm, 12 cm, and 13 cm. triangle def is similar to triangle rst. in triangle def,
the shortest side is 15 cm.
the scale factor from triangle rst to triangle def is
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Explanation:

Step1: Find the scale factor formula

The scale factor \(k\) of two similar triangles is the ratio of corresponding side lengths. If \(\triangle RST\sim\triangle DEF\), then \(k=\frac{\text{side length of }\triangle DEF}{\text{side length of }\triangle RST}\)

Step2: Identify the corresponding shortest sides

In \(\triangle RST\), the shortest side length \(a = 5\mathrm{cm}\). In \(\triangle DEF\), the shortest side length \(A=15\mathrm{cm}\)

Step3: Calculate the scale factor

Using the formula \(k=\frac{A}{a}\), substitute \(A = 15\) and \(a = 5\). So \(k=\frac{15}{5}=3\)

Answer:

\(3\)