Identify the given side lengths for Triangle P and the longest side for Triangle Q.

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here's the solution for the triangle problem:

Identify the given side lengths for Triangle P and the longest side for Triangle Q.
Triangle P has sides 5, 12, and 13. The longest side of Triangle P is 13.
Triangle Q has a longest side of $30 \text{ cm}$ .
Calculate the scale factor.
The scale factor is the ratio of the corresponding longest sides.
$\text{Scale factor} = \frac{\text{Longest side of Triangle Q}}{\text{Longest side of Triangle P}}$ $\text{Scale factor} = \frac{30}{13}$
Calculate the missing sides of Triangle Q.
Multiply each side of Triangle P by the scale factor to find the corresponding sides of Triangle Q.

For the side corresponding to 5:
$\text{Side}_1 \text{ of Q} = 5 \times \frac{30}{13} = \frac{150}{13} \text{ cm} \approx 11.54 \text{ cm}$
For the side corresponding to 12:
$\text{Side}_2 \text{ of Q} = 12 \times \frac{30}{13} = \frac{360}{13} \text{ cm} \approx 27.69 \text{ cm}$
The scale factor is $\boxed{\frac{30}{13}}$ and the missing sides of Triangle Q are $\boxed{\frac{150}{13} \text{ cm}}$ and $\boxed{\frac{360}{13} \text{ cm}}$ .

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