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The question asks whether \(\triangle XYZ\) is a scale drawing of \(\triangle RST\). To determine this, we need to check if the corresponding sides of the two triangles are proportional.

The side lengths of \(\triangle RST\) are:
- \(RS = 3 \frac{1}{2} = \frac{7}{2}\)
- \(ST = 5 \frac{1}{10} = \frac{51}{10}\)
- \(RT = 6 \frac{1}{4} = \frac{25}{4}\)

The side lengths of \(\triangle XYZ\) are:
- \(XY = 5 \frac{1}{4} = \frac{21}{4}\)
- \(YZ = 7 \frac{13}{20} = \frac{153}{20}\)
- \(XZ = 9 \frac{3}{8} = \frac{75}{8}\)

We now check the ratios of the corresponding sides:
1. \(\frac{RS}{XY} = \frac{\frac{7}{2}}{\frac{21}{4}} = \frac{7}{2} \times \frac{4}{21} = \frac{28}{42} = \frac{2}{3}\)
2. \(\frac{ST}{YZ} = \frac{\frac{51}{10}}{\frac{153}{20}} = \frac{51}{10} \times \frac{20}{153} = \frac{1020}{1530} = \frac{2}{3}\)
3. \(\frac{RT}{XZ} = \frac{\frac{25}{4}}{\frac{75}{8}} = \frac{25}{4} \times \frac{8}{75} = \frac{200}{300} = \frac{2}{3}\)

Since all corresponding sides have the same ratio, \(\frac{2}{3}\), \(\triangle XYZ\) is indeed a scale drawing of \(\triangle RST\), with a scale factor of \(\frac{2}{3}\).

Would you like more details on the calculations, or do you have any questions?

Here are 5 related questions:
1. How do we check if two triangles are similar using angles?
2. What other properties can confirm two triangles are scale drawings?
3. What happens if only two sides are proportional between triangles?
4. Can two triangles be congruent if their sides are proportional but not equal?
5. How do scale factors affect the areas of triangles?

**Tip:** Always check all corresponding sides when determining if two figures are scale drawings, to ensure proportionality.

Is triangle XYZ a scale drawing of triangle RST? Explain how you know.

Learn how to determine if triangle XYZ is a scale drawing of triangle RST using ratios of corresponding sides. This detailed solution covers geometric principles, proportionality, and similarity of triangles, suitable for students in Grades 8-10.

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